G. De Philippis, E. Paolini: A short proof of the minimality of Simons cone Rend. Sem. Mat. Univ. Padova Vol. 121, p. 233-241, 2009 G. De Philippis: Weak notions of Jacobian determinant and relaxation ESAIM Control Optim. Calc. Var (Accepted Paper) 2010 L. Ambrosio, G. De Philippis, B. Kirchheim: Regularity of optimal transport maps and partial differential inclusions Rend. Lincei - Mat. e Appl. () 2011 G. De Philippis, F. Maggi: Sharp stability inequalities for the Plateau problem J. Differential Geom. (Accepted Paper) 2011 L. Ambrosio, G. De Philippis, L. Martinazzi: Gamma-convergence of nonlocal perimeter functionals Manuscripta Math. Vol. 134, p. 377-403, 2011 F. Charro, G. De Philippis, A. Di Castro, D. Maximo: On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian Calc. Var. Partial Differential Equations (Accepted Paper) http://arxiv.org/abs/1108.0113 2011 L. Brasco, G. De Philippis, B. Ruffini: Spectral optimization for the Stekloff--Laplacian: the stability issue J. Funct. Anal. p. 28, 2011 G. De Philippis: Regularity of optimal transport maps and applications (Phd Thesis) 2012 L. Ambrosio, G. Crasta, V. De Cicco, G. De Philippis: A nonautonomous chain rule in $W^{1,p}$ and in $BV$ Manuscripta Math. (Accepted Paper) 2012 L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli: Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case Comm. Partial Differential Equations 2012 F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi: Rigidity of equality cases in Steiner's perimeter inequality Anal. PDE (Accepted Paper) http://arxiv.org/abs/1309.1639 2013 F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi: Essential connectedness and the rigidity problem for Gaussian symmetrization J. Eur. Math. Soc. (Accepted Paper) http://arxiv.org/abs/1304.4527 2013 G. De Philippis, A. Figalli: $W^{2,1}$ regularity for solutions of the Monge-Ampère equation Invent. Math. 2013 G. De Philippis, A. Figalli, O. Savin: A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere equation Math. Ann. 2013 G. De Philippis, A. Figalli: Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps Anal. PDE 2013 G. De Philippis, A. Figalli: Sobolev regularity for Monge-Ampère type equations SIAM J. Math. Anal. 2013 G. De Philippis, M. Marini: A note on Petty's Theorem Kodai Mathematical Journal (Accepted Paper) 2014 G. De Philippis, A. Figalli: Partial regularity results in optimal transportation (Springer INdAM series) 2014 G. De Philippis, F. Maggi: Dimensional estimates for singular sets in geometric variational problems with free boundaries J. Reine Angew. Math. (Accepted Paper) http://arxiv.org/abs/1407.4834 p. 15, 2014 G. Crasta, V. De Cicco, G. De Philippis: Kinetic formulation and uniqueness for scalar conservation laws with discontinuous flux Comm. in P.D.E. (Accepted Paper) http://arxiv.org/abs/1404.5837 p. 31, 2014 G. De Philippis, F. Maggi: Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law Arch. Ration. Mech. Anal. (Accepted Paper) http://arxiv.org/abs/1402.0549 2014 G. De Philippis, A. Figalli: The Monge-Ampère equation and its link to optimal transportation Bull. Amer. Math. Soc. (Accepted Paper) http://arxiv.org/abs/1310.6167 2014 G. De Philippis, B. Velichkov: Existence and regularity of minimizers for some spectral functionals with perimeter constraint Appl. Math. Optim. Vol. 69, N. 2, p. 199--231, 2014 L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli: A global existence result for the semigeostrophic equations in three dimensional convex domains Discrete Contin. Dyn. Syst. 2014 G. De Philippis, A. Figalli: Higher integrability for minimizers of the Mumford-Shah functional Arch. Ration. Mech. Anal. 2014 L. Brasco, G. De Philippis, B. Velichkov: Faber-Krahn inequalities in sharp quantitative form Duke Math. J. Vol. 164, N. 9, p. 1777-1832, 2015 G. De Philippis, N. Gigli: From volume cone to metric cone in the nonsmooth setting Geom. Funct. Anal. (Accepted Paper) http://arxiv.org/abs/1512.03113 2015 G. De Philippis, A. Figalli: Optimal regularity of the convex envelope Trans. Amer. Math. Soc. 2015 G. De Philippis, A. Figalli: Partial Regularity for optimal transport maps Publ. Math. Inst. Hautes Études Sci. 2015 G. De Philippis, A. Figalli: A note on the dimension of the singular set in free interface problems Differential Integral Equations 2015 G. De Philippis, A. R. Mészáros, F. Santambrogio, B. Velichkov: BV Estimates in Optimal Transportation and Applications Arch. Rat. Mech. Anal. 2015 G. De Philippis: On the singular part of measures constrained by linear PDEs and applications (Proceedings of the 7ECM) 2016 G. De Philippis, A. Marchese, F. Rindler: On a conjecture of Cheeger (Accepted Paper) http://arxiv.org/abs/1607.02554 2016 L. Brasco, G. De Philippis: Spectral inequalities in quantitative form (Book Chapter) http://arxiv.org/abs/1604.05072 p. 71, 2016 G. Crasta, V. De Cicco, G. De Philippis, F. Ghiraldin: Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness Arch. Ration. Mech. An. (Accepted Paper) http://arxiv.org/abs/1509.08273 2016 G. De Philippis, F. Rindler: Characterization of generalized Young measures generated by symmetric gradients Arch. Ration. Mech. An. (Accepted Paper) http://arxiv.org/abs/1604.04097 2016 G. De Philippis, F. Rindler: On the structure of ${\mathscr A}$-free measures and applications Ann. of Math. (Accepted Paper) http://arxiv.org/abs/1601.06543 2016 G. De Philippis, G. Franzina, A. Pratelli: Existence of isoperimetric sets with densities ''converging from below'' on $\mathbb R^N$ Journal of Geometric Analysis 2016 G. De Philippis, J. Lamboley, M. Pierre, B. Velichkov: Regularity of Minimizers of Shape Optimization Problems involving Perimeter J. Math. Pures Appl. 2016 G. De Philippis, S. Di Marino, M. Focardi: Lower semicontinuity for non-coercive polyconvex integrals in the limit case Proceedings of the Royal Society of Edinburgh Vol. 146A, p. 243--264, 2016 G. De Philippis, A. De Rosa, F. Ghiraldin: A direct approach to Plateau's problem in any codimension Adv. in Math. Vol. 288, p. 5980, 2016 A. Arroyo-Rabasa, G. De Philippis, F. Rindler: Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints Adv. Calc. Var (Accepted Paper) http://arxiv.org/abs/1701.02230 2017 G. De Philippis, F. Rindler: On the structure of measures constrained by linear PDEs (Proceedings) http://arxiv.org/abs/1712.08897 2017 G. De Philippis, N. Fusco, A. Pratelli: On the approximation of SBV functions Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 2017 C. De Lellis, G. De Philippis, J. Hirsch, A. Massaccesi: Boundary regularity of mass-minimizing integral currents and a question of Almgren Matrix Annals 2017 G. De Philippis, N. Gigli: Non-collapsed spaces with Ricci curvature bounded from below (Preprint) http://arxiv.org/abs/1708.02060 2017 G. De Philippis, A. Figalli: Rigidity and stability of Caffarelli's log-concave perturbation theorem Nonlinear Anal. 2017 A. Arroyo-Rabasa, G. De Philippis, J. Hirsch, F. Rindler: Dimensional estimates and rectifiability for measures satisfying linear PDE constraints Geom. Funct. Anal. (Accepted Paper) http://arxiv.org/abs/1811.01847 2018 G. De Philippis, T. Laux: Implicit time discretization for the mean curvature flow of outward minimizing sets Ann. Sc. Norm. Super. Pisa Cl. Sci (Accepted Paper) 2018 C. De Lellis, G. De Philippis, J. Hirsch, A. Massaccesi: On the boundary behavior of mass-minimizing integral currents To apper in Memoirs of the American Mathematical Society (Accepted Paper) http://arxiv.org/abs/1809.09457 2018 G. De Philippis, A. De Rosa, F. Ghiraldin: Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies Comm. Pure App. Math. 2018 G. De Philippis, M. Goldman: A two-point function approach to connectedness of drops in convex potentials CAG (Accepted Paper) http://arxiv.org/abs/1809.01513 2018 G. De Philippis, L. Palmieri, F. Rindler: On the two-state problem for general differential operators Nonlinear Anal. (Accepted Paper) http://arxiv.org/abs/1803.09302 2018 G. De Philippis, M. Marini, E. Mukoseeva: The sharp quantitative isocapacitary inequality (Submitted Paper) http://arxiv.org/abs/1901.11309 2019 G. De Philippis, A. De Rosa, J. Hirsch: The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals Discrete Contin. Dyn. Syst. 2019 G. De Philippis, J. Hirsch, G. Vescovo: Regularity of minimizers for a model of charged droplets Comm. Math. Phys. (Accepted Paper) http://arxiv.org/abs/1901.02546 2019 G. De Philippis, A. Pratelli: The closure of planar diffeomorphisms in Sobolev spaces Ann. Inst. H. Poincaré Anal. Non Linéaire (Accepted Paper) http://arxiv.org/abs/1710.07228 2019 G. De Philippis, J. Núñez-Zimbrón: The behavior of harmonic functions at singular points of $\mathsf{RCD}$ spaces (preprint) http://arxiv.org/abs/1909.05220 2019 C. De Lellis, G. De Philippis, J. Hirsch: Nonclassical minimizing surfaces with smooth boundary J. Differential Geom. (Accepted Paper) http://arxiv.org/abs/1906.09488 2019 C. De Lellis, G. De Philippis, B. Kirchheim, R. Tione: Geometric measure theory and differential inclusions Annales de la Faculte' des Sciences de Toulouse 2019 G. De Philippis, F. Rindler: Fine properties of functions of bounded deformation -- an approach via linear PDEs (Survey paper) http://arxiv.org/abs/1911.01356 2019 G. De Philippis, M. Marini, M. Mazzucchelli, S. Suhr: Closed geodesics on reversible Finsler 2-spheres (Preprint) http://arxiv.org/abs/2002.00415 2020 G. De Philippis, A. De Rosa, F. Ghiraldin: Existence results for minimizers of parametric elliptic functionals J. Geom. Anal. 2020 G. De Philippis, M. Engelstein, L. Spolaor, B. Velichkov: Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries (Preprint) http://arxiv.org/abs/2107.12485 2021 L. De Masi, G. De Philippis: Min-max construction of minimal surfaces with a fixed angle at the boundary (preprint) http://arxiv.org/abs/2111.09913 2021 A. Arroyo-Rabasa, G. De Philippis, J. Hirsch, F. Rindler, A. Skorobogatova: Higher integrability for measures satisfying a PDE constraint (preprint) http://arxiv.org/abs/2106.03077 2021 L. Brasco, G. De Philippis, G. Franzina: Positive solutions to the sublinear Lane-Emden equation are isolated Comm. Partial Differential Equations (Accepted Paper) http://arxiv.org/abs/1911.09163 p. 31, 2021 G. De Philippis, L. Spolaor, B. Velichkov: Regularity of the free boundary for the two-phase Bernoulli problem Inventiones mathematicae 2021 G. De Philippis, N. Fusco, M. Morini: Regularity of capillarity droplets with obstacle (Submitted Paper) 2022 G. De Philippis, A. Pigati: Non-degenerate minimal submanifolds as energy concentration sets: a variational approach (preprint) http://arxiv.org/abs/2205.12389 2022 G. De Philippis, A. Marchese, A. Merlo, A. Pinamonti, F. Rindler: On the converse of Pansu's Theorem ARMA (Accepted Paper) http://arxiv.org/abs/2211.06081 2022 G. De Philippis, A. De Rosa: The anisotropic Min-Max theory: Existence of anisotropic minimal and CMC surfaces Comm. Pure App. Math. 2023 G. De Philippis, C. Gasparetto, F. Schulze: A short proof of Allards and Brakkes regularity theorems International Mathematics Research Notices 2023 G. De Philippis, R. Tione: On singular strictly convex solutions to the Monge-Ampere equation Annali della Scuola Normale di Pisa - Classe di Scienze 2023 G. De Philippis, A. Guerra, R. Tione: Unique continuation for differential inclusions Annales de l'Institut Henri Poincaré C 2023 G. De Philippis, M. Goldman, B. Ruffini: From energy bounds to dimensional estimates in a branched transport model for type-I superconductors American Journal of Mathematics (Accepted Paper) 2023 G. De Philippis, A. Halavati, A. Pigati: Decay of excess for the abelian Higgs model (Submitted) http://arxiv.org/abs/2405.13953 2024 G. De Philippis, A. De Rosa, Y. Li: Existence and regularity of min-max anisotropic minimal hypersurfaces (preprint) http://arxiv.org/abs/2409.15232 2024 G. De Philippis, L. Spolaor, B. Velichkov: (Quasi-)conformal methods in two-dimensional free boundary problems J. Eur. Math. Soc. 2024 G. De Philippis, Y. Shenfeld: Optimal transport maps, majorization, and log-subharmonic measures (Preprint) http://arxiv.org/abs/2411.12109 2024