Publications

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.