Publications

Quantitative convergence rates for scaling limit of SPDEs with transport noise

F. Flandoli; L. Galeati; D. Luo 

Journal Of Differential Equations. 2024-06-15. Vol. 394, p. 237-277. DOI : 10.1016/j.jde.2024.02.053.

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

C. J. P. Johansson 

Transactions Of The American Mathematical Society. 2024-05-15. DOI : 10.1090/tran/9090.

CONTROL OF HYPERBOLIC AND PARABOLIC EQUATIONS ON NETWORKS AND SINGULAR LIMITS

J. A. Barcena-Petisco; M. Cavalcante; G. M. Coclite; N. De Nitti; E. Zuazua 

Mathematical Control And Related Fields. 2024-04-24. DOI : 10.3934/mcrf.2024015.

Infinite-width limit of deep linear neural networks

L. Chizat; M. Colombo; X. Fernandez-Real; A. Figalli 

Communications On Pure And Applied Mathematics. 2024-05-06. DOI : 10.1002/cpa.22200.

Stability Threshold of the 2D Couette Flow in a Homogeneous Magnetic Field Using Symmetric Variables

M. Dolce 

Communications In Mathematical Physics. 2024-04-01. Vol. 405, num. 4, p. 94. DOI : 10.1007/s00220-024-04982-z.

Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings

G. M. Coclite; N. De Nitti; F. Maddalena; G. Orlando; E. Zuazua 

Mathematical Models & Methods In Applied Sciences. 2024-04-20. DOI : 10.1142/S021820252450026X.

Generic regularity of free boundaries for the thin obstacle problem

X. Fernandez-Real; C. Torres-Latorre 

Advances In Mathematics. 2023-10-04. Vol. 433, p. 109323. DOI : 10.1016/j.aim.2023.109323.

MIXING FOR GENERIC ROUGH SHEAR FLOWS

L. Galeati; M. Gubinelli 

Siam Journal On Mathematical Analysis. 2023-01-01. Vol. 55, num. 6, p. 7240-7272. DOI : 10.1137/23M155222X.

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

J. Pitcho; M. Sorella 

Siam Journal On Mathematical Analysis. 2023-01-01. Vol. 55, num. 5, p. 4640-4663. DOI : 10.1137/22M1487187.

SMOOTH APPROXIMATIONS FOR FULLY NONLINEAR NONLOCAL ELLIPTIC EQUATIONS

X. Fernandez-Real 

Transactions Of The American Mathematical Society. 2023-10-19. DOI : 10.1090/tran/9038.

Gluing Non-unique Navier-Stokes Solutions

D. Albritton; E. Brue; M. Colombo 

Annals Of Pde. 2023-12-01. Vol. 9, num. 2, p. 17. DOI : 10.1007/s40818-023-00155-8.

Sharp bounds on enstrophy growth for viscous scalar conservation laws

D. Albritton; N. De Nitti 

Nonlinearity. 2023-12-01. Vol. 36, num. 12, p. 7142-7148. DOI : 10.1088/1361-6544/ad073f.

Anomalous Dissipation and Lack of Selection in the Obukhov-Corrsin Theory of Scalar Turbulence

M. Colombo; G. Crippa; M. Sorella 

Annals Of Pde. 2023-12-01. Vol. 9, num. 2, p. 21. DOI : 10.1007/s40818-023-00162-9.

Graphical solutions to one-phase free boundary problems

M. Engelstein; X. Fernandez-Real; H. Yu 

Journal Fur Die Reine Und Angewandte Mathematik. 2023-10-27. Vol. 2023, num. 804, p. 155-195. DOI : 10.1515/crelle-2023-0067.

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

X. Fernandez-Real; R. Tione 

Proceedings Of The American Mathematical Society. 2023-09-14. Vol. 151, num. 12, p. 5283-5297. DOI : 10.1090/proc/16490.

Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations

J. Bedrossian; R. Bianchini; M. C. Zelati; M. Dolce 

Communications On Pure And Applied Mathematics. 2023-07-03. DOI : 10.1002/cpa.22123.

Global Regularity For The Nonlinear Wave Equation With Slightly Supercritical Power

M. Colombo; S. Haffter 

Analysis & Pde. 2023-01-01. Vol. 16, num. 3, p. 613-642. DOI : 10.2140/apde.2023.16.613.

LDP and CLT for SPDEs with transport noise

L. Galeati; D. Luo 

Stochastics And Partial Differential Equations-Analysis And Computations. 2023-03-28. DOI : 10.1007/s40072-023-00292-y.

Stability estimates for singular SDEs and applications

L. Galeati; C. Ling 

Electronic Journal of Probability. 2023-02-09. Vol. 28, num. none. DOI : 10.1214/23-EJP913.

T-5 configurations and hyperbolic systems

C. J. P. Johansson; R. Tione 

Communications In Contemporary Mathematics. 2023-01-13. DOI : 10.1142/S021919972250081X.

Distribution dependent SDEs driven by additive fractional Brownian motion

L. Galeati; F. A. Harang; A. Mayorcas 

Probability Theory and Related Fields. 2022-05-20. Vol. 185, num. 1-2, p. 251-309. DOI : 10.1007/s00440-022-01145-w.

Distribution dependent SDEs driven by additive continuous noise

L. Galeati; F. A. Harang; A. Mayorcas 

Electronic Journal of Probability. 2022-03-03. Vol. 27, p. 37, 1-38. DOI : 10.1214/22-EJP756.

Regularization of multiplicative SDEs through additive noise

L. Galeati; F. A. Harang 

The Annals of Applied Probability. 2022-10-18. Vol. 32, num. 5, p. 3930-3963. DOI : 10.1214/21-AAP1778.

Eddy heat exchange at the boundary under white noise turbulence

F. Flandoli; L. Galeati; D. Luo 

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2022-01-31. Vol. 380, num. 2219. DOI : 10.1098/rsta.2021.0096.

Nonsmooth and nonenergetic solutions of PDE’s through convex integration

C. J. P. Johansson 

2022.

Typicality results for weak solutions of the incompressible Navier-Stokes equations

M. Colombo; L. De Rosa; M. Sorella 

Esaim-Control Optimisation And Calculus Of Variations. 2022-06-14. Vol. 28, p. 38. DOI : 10.1051/cocv/2022038.

Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

T. Buckmaster; M. Colombo; V. Vicol 

Journal Of The European Mathematical Society. 2022-01-01. Vol. 24, num. 9, p. 3333-3378. DOI : 10.4171/JEMS/1162.

Sharp Energy Regularity And Typicality Results For Holder Solutions Of Incompressible Euler Equations

L. De Rosa; R. Tione 

Analysis & Pde. 2022-01-01. Vol. 15, num. 2, p. 405-428. DOI : 10.2140/apde.2022.15.405.

Non-Uniqueness Of Integral Curves For Autonomous Hamiltonian Vector Fields

V. Giri; M. Sorella 

Differential And Integral Equations. 2022-07-01. Vol. 35, num. 7-8, p. 411-436. DOI : 10.57262/die035-0708-411.

On the commutativity of flows of rough vector fields

M. Colombo; R. Tione 

Journal De Mathematiques Pures Et Appliquees. 2022-03-01. Vol. 159, p. 294-312. DOI : 10.1016/j.matpur.2021.12.005.

Blow-up, partial regularity and turbulence in incompressible fluid dynamics

S. N. A. Haffter / M. Colombo (Dir.)  

Lausanne, EPFL, 2022. 

Noiseless regularisation by noise

L. Galeati; M. Gubinelli 

Revista Matemática Iberoamericana. 2021-07-06. Vol. 38, num. 2, p. 433-502. DOI : 10.4171/RMI/1280.

Obesity-associated deficits in inhibitory control are phenocopied to mice through gut microbiota changes in one-carbon and aromatic amino acids metabolic pathways

M. Arnoriaga-Rodriguez; J. Mayneris-Perxachs; O. Contreras-Rodriguez; A. Burokas; J-A. Ortega-Sanchez et al. 

Gut. 2021-12-01. Vol. 70, num. 12, p. 2283-2296. DOI : 10.1136/gutjnl-2020-323371.

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

X. Fernandez-Real; Y. Jhaveri 

Analysis & Pde. 2021-01-01. Vol. 14, num. 5, p. 1599-1669. DOI : 10.2140/apde.2021.14.1599.

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem

M. Colombo; L. Spolaor; B. Velichkov 

Interfaces And Free Boundaries. 2021-01-01. Vol. 23, num. 2, p. 159-167. DOI : 10.4171/IFB/452.

Non-smooth solutions in incompressible fluid dynamics

L. De Rosa / M. Colombo; C. De Lellis (Dir.)  

Lausanne, EPFL, 2021. 

Iron status influences non-alcoholic fatty liver disease in obesity through the gut microbiome

J. Mayneris-Perxachs; M. Cardellini; L. Hoyles; J. Latorre; F. Davato et al. 

Microbiome. 2021-05-07. Vol. 9, num. 1, p. 104. DOI : 10.1186/s40168-021-01052-7.

On the constancy theorem for anisotropic energies through differential inclusions

J. Hirsch; R. Tione 

Calculus of Variations and Partial Differential Equations. 2021-04-21. Vol. 60, num. 3, p. 86. DOI : 10.1007/s00526-021-01981-z.

Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves

E. Brue; M. Colombo; C. De Lellis 

Archive For Rational Mechanics And Analysis. 2021-03-08. Vol. 240, p. 1055–1090. DOI : 10.1007/s00205-021-01628-5.

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

M. C. Colombo; S. N. A. Haffter 

Annals of PDE. 2021-03-26. Vol. 7, num. 1, p. 6. DOI : 10.1007/s40818-021-00093-3.

Linear Lipschitz and C-1 extension operators through random projection

E. Brue; S. Di Marino; F. Stra 

Journal Of Functional Analysis. 2021-02-15. Vol. 280, num. 4, p. 108868. DOI : 10.1016/j.jfa.2020.108868.

On the Well-Posedness of Branched Transportation

M. Colombo; A. De Rosa; A. Marchese 

Communications On Pure And Applied Mathematics. 2021. Vol. 74, num. 4, p. 833-864. DOI : 10.1002/cpa.21919.

Obesity Impairs Short-Term and Working Memory through Gut Microbial Metabolism of Aromatic Amino Acids

M. Arnoriaga-Rodriguez; J. Mayneris-Perxachs; A. Burokas; O. Contreras-Rodriguez; G. Blasco et al. 

Cell Metabolism. 2020-10-06. Vol. 32, num. 4, p. 548-+. DOI : 10.1016/j.cmet.2020.09.002.

On the asymptotic behavior of the solutions to parabolic variational inequalities

M. Colombo; L. Spolaor; B. Velichkov 

Journal Fur Die Reine Und Angewandte Mathematik. 2020-11-01. Vol. 768, p. 149-182. DOI : 10.1515/crelle-2019-0041.

Lagrangian Discretization Of Crowd Motion And Linear Diffusion

H. Leclerc; Q. Merigot; F. Santambrogio; F. Stra 

Siam Journal On Numerical Analysis. 2020-01-01. Vol. 58, num. 4, p. 2093-2118. DOI : 10.1137/19M1274201.

Regularity In Time Of Holder Solutions Of Euler And Hypodissipative Navier-Stokes Equations

M. Colombo; L. De Rosa 

Siam Journal On Mathematical Analysis. 2020-01-01. Vol. 52, num. 1, p. 221-238. DOI : 10.1137/19M1259900.

Direct Epiperimetric Inequalities for the Thin Obstacle Problem and Applications

M. Colombo; L. Spolaor; B. Velichkov 

Communications on Pure and Applied Mathematics. 2020-02-01. Vol. 73, num. 2, p. 384-420. DOI : 10.1002/cpa.21859.

The Generalized Caffarelli‐Kohn‐Nirenberg Theorem for the Hyperdissipative Navier‐Stokes System

M. Colombo; C. De Lellis; A. Massaccesi 

Communications on Pure and Applied Mathematics. 2020. Vol. 73, num. 3, p. 609-663. DOI : 10.1002/cpa.21865.

Stability for the mailing problem

M. Colombo; A. De Rosa; A. Marchese 

Journal de Mathématiques Pures et Appliquées. 2019-08-01. Vol. 128, p. 152-182. DOI : 10.1016/j.matpur.2019.01.020.

Quantitative estimate on singularities in isoperimetric clusters

M. Colombo; L. Spolaor 

Communications in Analysis and Geometry. 2019. Vol. 27, num. 6, p. 1233-1249. DOI : 10.4310/CAG.2019.v27.n6.a2.

On the Singular Local Limit for Conservation Laws with Nonlocal Fluxes

M. Colombo; G. Crippa; L. V. Spinolo 

Archive for Rational Mechanics and Analysis. 2019-09-01. Vol. 233, num. 3, p. 1131-1167. DOI : 10.1007/s00205-019-01375-8.

Regularity results for rough solutions of the incompressible Euler equations via interpolation methods

L. Forcella; M. Colombo; L. De Rosa 

Nonlinearity. 2019-10-02. Vol. 33, num. 9, p. 4818-4836. DOI : 10.1088/1361-6544/ab8fb5.

Continuity Of Multimarginal Optimal Transport With Repulsive Cost

M. Colombo; S. Di Marino; F. Stra 

Siam Journal On Mathematical Analysis. 2019-01-01. Vol. 51, num. 4, p. 2903-2926. DOI : 10.1137/19M123943X.

Regularity for general functionals with double phase

P. Baroni; M. Colombo; G. Mingione 

Calculus of Variations and Partial Differential Equations. 2018-04-01. Vol. 57, num. 2, p. 62. DOI : 10.1007/s00526-018-1332-z.

Improved stability of optimal traffic paths

M. Colombo; A. De Rosa; A. Marchese 

Calculus of Variations and Partial Differential Equations. 2018-02-01. Vol. 57, num. 1, p. 28. DOI : 10.1007/s00526-017-1299-1.

Ill-Posedness of Leray Solutions for the Hypodissipative Navier–Stokes Equations

M. Colombo; C. De Lellis; L. De Rosa 

Communications in Mathematical Physics. 2018-09-01. Vol. 362, num. 2, p. 659-688. DOI : 10.1007/s00220-018-3177-x.

A logarithmic epiperimetric inequality for the obstacle problem

M. Colombo; L. Spolaor; B. Velichkov 

Geometric and Functional Analysis. 2018-05-11. Vol. 28, num. 4, p. 1029-1061. DOI : 10.1007/s00039-018-0451-1.

Lipschitz changes of variables between perturbations of log-concave measures

M. Colombo; A. Figalli; Y. Jhaveri 

Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze. 2017. Vol. 17, num. 4, p. 1491-1519. DOI : 10.2422/2036-2145.201510_009.

Optimality of integrability estimates for advection–diffusion equations

S. Bianchini; M. Colombo; G. Crippa; L. V. Spinolo 

Nonlinear Differential Equations and Applications NoDEA. 2017-08-01. Vol. 24, num. 4, p. 33. DOI : 10.1007/s00030-017-0455-9.

On the lower semicontinuous envelope of functionals defined on polyhedral chains

M. Colombo; A. De Rosa; A. Marchese; S. Stuvard 

Nonlinear Analysis. 2017-11-01. Vol. 163, p. 201-215. DOI : 10.1016/j.na.2017.08.002.

On the Lagrangian structure of transport equations: The Vlasov–Poisson system

L. Ambrosio; M. Colombo; A. Figalli 

Duke Mathematical Journal. 2017-12-01. Vol. 166, num. 18, p. 3505-3568. DOI : 10.1215/00127094-2017-0032.

Existence and almost everywhere regularity of isoperimetric clusters for fractional perimeters

M. Colombo; F. Maggi 

Nonlinear Analysis: Theory, Methods & Applications. 2017. Vol. 153, p. 243-274. DOI : 10.1016/j.na.2016.09.019.

Essential connectedness and the rigidity problem for Gaussian symmetrization

F. Cagnetti; M. Colombo; G. De Philippis; F. Maggi 

Journal of the European Mathematical Society. 2017. Vol. 19, num. 2, p. 395-439. DOI : 10.4171/JEMS/669.

Non-autonomous functionals, borderline cases and related function classes

P. Baroni; M. Colombo; G. Mingione 

St. Petersburg Mathematical Journal. 2016-03-30. Vol. 27, num. 3, p. 347-379. DOI : 10.1090/spmj/1392.

Minimizing movements along a sequence of functionals and curves of maximal slope

A. Braides; M. Colombo; M. Gobbino; M. Solci 

Comptes Rendus Mathematique. 2016-07-01. Vol. 354, num. 7, p. 685-689. DOI : 10.1016/j.crma.2016.04.011.

Logarithmic estimates for continuity equations

M. Colombo; G. Crippa; S. Spirito 

Networks and Heterogeneous Media. 2016-03-01. Vol. 11, num. 2, p. 301-311. DOI : 10.3934/nhm.2016.11.301.

Counterexamples in multimarginal optimal transport with Coulomb cost and spherically symmetric data

M. Colombo; F. Stra 

Mathematical Models and Methods in Applied Sciences. 2016-06-15. Vol. 26, num. 06, p. 1025-1049. DOI : 10.1142/S021820251650024X.

Calderón–Zygmund estimates and non-uniformly elliptic operators

M. Colombo; G. Mingione 

Journal of Functional Analysis. 2016-02-15. Vol. 270, num. 4, p. 1416-1478. DOI : 10.1016/j.jfa.2015.06.022.

Multimarginal Optimal Transport Maps for One-dimensional Repulsive Costs

M. Colombo; L. De Pascale; S. Di Marino 

Canadian Journal of Mathematics-Journal Canadien De Mathematiques. 2015-04-01. Vol. 67, num. 2, p. 350-368. DOI : 10.4153/CJM-2014-011-x.

Renormalized solutions to the continuity equation with an integrable damping term

M. Colombo; G. Crippa; S. Spirito 

Calculus of Variations and Partial Differential Equations. 2015-10-01. Vol. 54, num. 2, p. 1831-1845. DOI : 10.1007/s00526-015-0845-y.

Regularity for Double Phase Variational Problems

M. Colombo; G. Mingione 

Archive for Rational Mechanics and Analysis. 2015-02-01. Vol. 215, num. 2, p. 443-496. DOI : 10.1007/s00205-014-0785-2.

Harnack inequalities for double phase functionals

P. Baroni; M. Colombo; G. Mingione 

Nonlinear Analysis: Theory, Methods & Applications. 2015-07-01. Vol. 121, p. 206-222. DOI : 10.1016/j.na.2014.11.001.

Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

L. Ambrosio; M. Colombo; A. Figalli 

Archive for Rational Mechanics and Analysis. 2015-11-01. Vol. 218, num. 2, p. 1043-1081. DOI : 10.1007/s00205-015-0875-9.

Equality between Monge and Kantorovich multimarginal problems with Coulomb cost

M. Colombo; S. Di Marino 

Annali di Matematica Pura ed Applicata. 2015-04-01. Vol. 194, num. 2, p. 307-320. DOI : 10.1007/s10231-013-0376-0.

Bounded Minimisers of Double Phase Variational Integrals

M. Colombo; G. Mingione 

Archive for Rational Mechanics and Analysis. 2015-10-01. Vol. 218, num. 1, p. 219-273. DOI : 10.1007/s00205-015-0859-9.

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

L. Ambrosio; M. Colombo; S. Di Marino; L. Ambrosio; Y. Giga et al. 

2015. Variational Methods for Evolving Objects, Hokkaido University, Sapporo, Japan, July 30–August 3, 2012. p. 1-58. DOI : 10.2969/aspm/06710001.

An Excess-Decay Result for a Class of Degenerate Elliptic Equations

M. Colombo; A. Figalli 

Discrete and Continuous Dynamical Systems-Series S. 2014-08-01. Vol. 7, num. 4, p. 631-652. DOI : 10.3934/dcdss.2014.7.631.

Rigidity of equality cases in Steiner’s perimeter inequality

F. Cagnetti; M. Colombo; G. De Philippis; F. Maggi 

Analysis & PDE. 2014-12-12. Vol. 7, num. 7, p. 1535-1593. DOI : 10.2140/apde.2014.7.1535.

Regularity results for very degenerate elliptic equations

M. Colombo; A. Figalli 

Journal de Mathématiques Pures et Appliquées. 2014. Vol. 101, num. 1, p. 94-117. DOI : 10.1016/j.matpur.2013.05.005.

Obstructions to regularity in the classical Monge problem

M. Colombo; E. Indrei 

Mathematical Research Letters. 2014. Vol. 21, num. 4, p. 697-712. DOI : 10.4310/MRL.2014.v21.n4.a6.

A Global Existence Result for the Semigeostrophic Equations in Three Dimensional Convex Domains

L. Ambrosio; M. Colombo; G. De Philippis; A. Figalli 

Discrete and Continuous Dynamical Systems. 2014-04-01. Vol. 34, num. 4, p. 1251-1268. DOI : 10.3934/dcds.2014.34.1251.

Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow

M. Colombo; M. Gobbino 

Mathematical Models and Methods in Applied Sciences. 2012-08-01. Vol. 22, num. 08, p. 1250017. DOI : 10.1142/S0218202512500170.

Multiple Object Tracking via Prediction and Filtering with a Sobolev-Type Metric on Curves

E. Bardelli; M. Colombo; A. Mennucci; A. Yezzi; A. Fusiello et al. 

Computer Vision – Eccv 2012: Workshops and Demonstrations, Pt I; Berlin, Heidelberg: Springer, 2012. p. 143-152.

Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case

L. Ambrosio; M. Colombo; G. De Philippis; A. Figalli 

Communications in Partial Differential Equations. 2012. Vol. 37, num. 12, p. 2209-2227. DOI : 10.1080/03605302.2012.669443.

Slow Time Behavior of the Semidiscrete Perona–Malik Scheme in One Dimension

M. Colombo; M. Gobbino 

SIAM Journal on Mathematical Analysis. 2011-11-10. Vol. 43, num. 6, p. 2564-2600. DOI : 10.1137/100818698.

All my research papers are available at cvgmt and arvix.

  1. Anomalous Dissipation and Lack of Selection in the Obukhov-Corrsin Theory of Scalar Turbulence (with G. Crippa, M. Sorella). Submitted paper.
  2. Nonlocal traffic models with general kernels: singular limit, entropy admissibility, and convergence rate (with G. Crippa, E. Marconi, L. Spinolo). Submitted paper.
  3. Gluing non-unique Navier-Stokes solutions (with D. Albritton, E. Bru ́e). Submitted paper.
  4. Improved Hausdorff dimension estimate of the singular set of the supercritical surface quasi-geostrophic equation (with S. Haffter). Submitted paper.
  5. A transmission problem for (p, q)-Laplacian (with S. Kim, H. Shahgholian). Submitted paper.
  6. Non-uniqueness of Leray solutions of the forced Navier-Stokes equations (with D. Albritton and E. Bru ́e). Ann. of Math., 196 (2022), 415–455.
  7. Instability and nonuniqueness for the 2d Euler equations in vorticity form, after M. Vishik (with D. Albritton, E. Bru ́e, C. De Lellis, V. Giri, M. Janish and H. Kwon). Submitted paper.
  8. Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space (with E. Bru ́e). Submitted paper.
  9. Non-classical solutions of the p-Laplace equation (with R. Tione). Submitted paper.
  10. Optimal regularity for the fully nonlinear thin obstacle problem (with X. Fern ́andez-Real and X. Ros-Oton). Submitted paper.
  11. First order expansion in the semiclassical limit of the Levy-Lieb functional (with S. Di Marino and F. Stra). Submitted paper.
  12. Typicality results for weak solutions of the incompressible Navier–Stokes equations (with L. De Rosa and M. Sorella). ESAIM Control Optim. Calc. Var., 28 (2022), Paper No. 38, 24 pp.
  13. On the commutativity of flows of rough vector fields (with R. Tione). J. Math. Pures Appl., 159 (2022), 294–312.
  14. Estimate on the dimension of the singular set of the supercritical surface quasigeostrophic equation (with S. Haffter). Ann. PDE., 7 (2021), Paper No. 6, 62 pp.
  15. Positive solutions of transport equations and classical nonuniqueness of characteristic curves (with E. Bruè, C. De Lellis). Arch. Ration. Mech. Anal., 240 (2021), 1055–1090.
  16. Local limit of nonlocal traffic models: convergence results and total variation blow-up (with G. Crippa, E. Marconi and L. V. Spinolo). Ann. Inst. H. Poincar ́e C Anal. Non Lineaire, 38 (2021), 1653–1666.
     
  17. Mixing and diffusion for rough shear flows (with M. Coti Zelati, K. Widmayer). Ars Inven. Anal. 2021, Paper No. 2, 21 pp.
  18. Stability of optimal traffic plans in the irrigation problem (with A. De Rosa, A. Marchese, P. Pegon, A. Prouff). Discrete Contin. Dyn. Syst., 42 (2022), 1647–1667.
  19. Global regularity for the hyperdissipative Navier-Stokes equation below the critical order (with S. Haffter). J. Dierential Equations, 275 (2021), 815-836.
  20. Global regularity for the nonlinear wave equation with slightly supercritical power (with S. Haffter).Submitted paper .
  21. Bounds on optimal transport maps onto log-concave measures (with M. Fathi). J. Dierential Equations, 271 (2021), 1007-1022.
  22. Regularity results for rough solutions of the incompressible Euler equations via interpolation methods (with L. De Rosa, L. Forcella). Nonlinearity, 33 (2020), 4818-4836.
  23. Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem (with L. Spolaor, B. Velichkov). Interfaces Free Bound., 23 (2021), 159–167.
  24. On the well-posedness of branched transportation (with A. De Rosa, A. Marchese). Comm. Pure Appl. Math., 74 (2021), 833–864.
  25. On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws (with G. Crippa, M. Graff, L. Spinolo). ESAIM Math. Model. Numer. Anal., 55 (2021), 2705–2723.
  26. Recent results on the singular local limit for nonlocal conservation laws (with G. Crippa, M. Graff, L. Spinolo). To appear in Proceedings of the 17-th Conference on Hyperbolic Problems – Hyperbolic Problems: Theory, Numerics, Applications.
  27. Regularity in time of Hölder solutions of Euler and hypodissipative Navier-Stokes equations (with L. De Rosa). SIAM J. Math. Anal., 52 (2020), 221-238.
  28. Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1 (with T. Buckmaster, V. Vicol). European Math. Soc.(JEMS), 24 (2022), 3333–3378.
  29. Stability of optimal traffic plans in the irrigation problem (with A. De Rosa, A. Marchese, P. Pegon, A. Prouff). Discrete Contin. Dyn. Syst., 42 (2022), 1647–1667.
  30. On the asymptotic behavior of the solutions to parabolic variational inequalities (with L. Spolaor, B. Velichkov). J. Reine Angew. Math., 768 (2020), 149-182.
  31. The singular set of minimal surfaces near polyhedral cones (with N. Edelen, L. Spolaor). To appear in J. Differential Geom.
  32. The generalized Caffarelli-Kohn-Nirenberg Theorem for the hyperdissipative Navier-Stokes system (with C. De Lellis, A. Massaccesi). Comm. Pure Applied Math., 73 (2020), no. 3, 609–663.
  33. Direct epiperimetric inequalities for the thin obstacle problem and applications (with L. Spolaor, B. Velichkov). Comm. Pure Applied Math., 73 (2020), no. 2, 384–420.
  34. Quantitative estimate on singularities in isoperimetric clusters (with L. Spolaor). Comm. Anal. Geom., 27 (2019), no. 6, 1233–1249.
  35. On the singular local limit for conservation laws with non local fluxes (with G. Crippa, L. Spinolo). Arch. Ration. Mech. Anal., 233 (2019), no. 3, 1131–1167.
  36. Stability for the mailing problem (with A. De Rosa and A. Marchese). J. Math. Pures Appl., 128 (2019), 152-182.
  37. Continuity of multi-marginal optimal transport with repulsive cost (with S. Di Marino, F. Stra). SIAM J. Math. Anal., 51 (2019), no. 4, 2903–2926.
  38. A logarithmic epiperimetric inequality for the obstacle problem (with L. Spolaor, B. Velichkov). Geom. Funct. Anal, 28 (2018), no. 4, 1029-1061.
  39. Regularity for general functionals with double phase (with P. Baroni, G. Mingione). Calc. Var. Partial Differential Equations, 57 (2018), no. 2, Art. 62, 48 pp..
  40. Ill-posedness of Leray solutions for the ipodissipative Navier–Stokes equations (with C. De Lellis, L. De Rosa). Comm. Math. Phys., 362 (2018), no. 2, 659–688.
  41. Improved stability of optimal traffic paths (with A. De Rosa and A. Marchese). Calc. Var. Partial Differential Equations, 57 (2018), no. 1, Art. 28, 33 pp..
  42. On the lower semicontinuous envelope of functionals defined on polyhedral chains (with A. De Rosa, A. Marchese, S. Stuvard). Nonlinear Anal., 163 (2017), 201–215.
  43. Optimality of integrability estimates for advection-diffusion equations (with S. Bianchini, G. Crippa, L. Spinolo). NoDEA Nonlinear Differential Equations Appl., 24 (2017), no. 4, Art. 33, 19 pp..
  44. Existence and almost everywhere regularity of isoperimetric clusters for fractional perimeters (with F. Maggi). Nonlinear Anal., 153 (2017), 243–274.
  45. Lipschitz Changes of Variables between Perturbations of Log-concave Measures (with A. Figalli and Y. Jhaveri). Ann. Sc. Norm. Super. Pisa Cl. Sci., 17 (2017), no. 4, 1491–1519.
  46. On the Lagrangian structure of transport equations: the Vlasov-Poisson system (with L. Ambrosio, A. Figalli). Duke Math. J., 166 (2017), no. 18, 3505–3568.
  47. Essential connectedness and the rigidity problem for Gaussian symmetrization (with F. Cagnetti, G. De Philippis, F. Maggi). J. Eur. Math. Soc. (JEMS), 19 (2017), no. 2, 395–439.
  48. Minimizing movements along a sequence of functionals and curves of maximal slope (with A. Braides, M. Gobbino, and M. Solci). C. R. Math. Acad. Sci. Paris, 354 (2016), noi.7, 685–689.
  49. Counterexamples in multimarginal optimal transport with Coulomb cost and radially symmetric data (with F. Stra). Math. Models Methods Appl. Sci., 26 (2016), no.  6, 1025–1049.
  50. Logarithmic estimates for continuity equations (with G. Crippa, S. Spirito). Netw. Heterog. Media, 11 (2016), no. 2, 301–311.
  51. Non-autonomous functionals, borderline cases and related function classes (with P. Baroni, G. Mingione). St. Petersburg Math. J., 27 (2016), no. 3, 347–379.
  52. Calderon-Zygmund estimates and non-uniformly elliptic operators (with G. Mingione). J. Funct. Anal., 270 (2015), no. 4, 1416–1478.
  53. Renormalized solutions to the continuity equation with an integrable damping term (with G. Crippa, S. Spirito). Calc. Var. Partial Differential Equations, 54 (2015), no. 2, 1831–1845.
  54. Harnack inequalities for double phase functionals (with P. Baroni, G. Mingione). Nonlinear Anal., 121 (2015), special issue in honor of Enzo Mitidieri for his 60th birthday, 206–222.
  55. Bounded minimisers of double phase variational integrals (with G. Mingione). Arch. Ration. Mech. Anal., 218 (2015), no. 1, 219–273.
  56. Existence and uniqueness of maximal regular flows for non-smooth vector fields (with L. Ambrosio, A. Figalli). Arch. Ration. Mech. Anal., 218 (2015), no. 2, 1043–1081.
  57. Regularity for double phase variational problems (with G. Mingione). Arch. Ration. Mech. Anal., 215 (2015), no. 2, 443–496.
  58. Multimarginal optimal transport maps for 1-dimensional repulsive costs (with S. Di Marino, L. De Pascale). Canad. J. Math., 67 (2015), no. 2, 350–368.
  59. Equality between Monge and Kantorovich multimarginal problems with Coulomb cost (with S. Di Marino). Ann. Mat. Pura Appl., 194 (2015), no. 2, 307–320.
  60. Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope (with L. Ambrosio, S. Di Marino). Adv. Stud. Pure Math., 67 (2015), Variational Methods for Evolving Objects, 1–58.
  61. An excess-decay result for a class of degenerate elliptic equations (with A. Figalli). Discr. Contin. Dyn. Syst. Ser. S, 7 (2014), no. 4, 631–652.
  62. Rigidity of equality cases in Steiner’s perimeter inequality (with F. Cagnetti, G. De Philippis, F. Maggi). Anal. PDE, 7 (2014), no. 7, 1535–1593.
  63. Obstructions to regularity in the classical Monge problem (with E. Indrei). Math. Res. Lett., 21 (2014), 697–712.
  64. Regularity results for very degenerate elliptic equations (with A. Figalli). J. Math. Pures Appl., 101 (2014), no. 1, 94–117.
  65. A global existence result for the semigeostrophic equations in three dimensional convex domains (with L. Ambrosio, G. De Philippis, A. Figalli). Discr. Contin. Dyn. Syst., 34 (2014), no. 4, special issue on Optimal Transport, 1251–1268.
  66. Multiple object tracking via prediction and filtering with a Sobolev-type metric on curves (with E. Bardelli, A. Mennucci, A. Yezzi). Computer Vision ECCV 2012. Workshops and Demonstrations, Lecture Notes in Computer Science, 7583 (2012), 143–152.
  67. Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (with L. Ambrosio, G. De Philippis, A. Figalli). Comm. Partial Differential Equations, 37 (2012), no. 12, 2209–2227.
  68. Passing to the limit in maximal slope curves: from a regularized Perona-Malik equation to the total variation flow (with M. Gobbino). Math. Models Methods Appl. Sci., 22 (2012), no. 8, 1250017, 19 pp..
  69. Slow time behavior of the semidiscrete Perona-Malik scheme in dimension one (with M. Gobbino). SIAM J. Math. Anal., 43 (2011), no. 6, 2564–2600.