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) 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 G. De Philippis, A. Figalli: Sobolev regularity for Monge-Ampère type equations SIAM J. Math. Anal. (Accepted Paper) 2012 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. (Accepted Paper) 2012 G. De Philippis, A. Figalli, O. Savin: A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere equation Math. Ann. (Accepted Paper) 2012 G. De Philippis, A. Figalli: Second order stability for the Monge-Ampere equation and strong Sobolev convergence of optimal transport maps Anal. PDE (Accepted Paper) 2012 G. De Philippis, A. Figalli: $W^{2,1}$ regularity for solutions of the Monge-Ampère equation Invent. 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 (Accepted Paper) 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 G. De Philippis, A. Figalli: Optimal regularity of the convex envelope Trans. Amer. Math. Soc. (Accepted Paper) 2013 F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi: Rigidity of equality cases in Steiner's perimeter inequality Anal. PDE (Accepted Paper) 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) 2013 G. De Philippis, A. Figalli: Higher integrability for minimizers of the Mumford-Shah functional Arch. Ration. Mech. Anal. (Accepted Paper) 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) p. 15, 2014 G. De Philippis, A. Figalli: A note on the dimension of the singular set in free interface problems Differential Integral Equations (Accepted Paper) 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) 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) 2014 G. De Philippis, A. Figalli: The Monge-Ampère equation and its link to optimal transportation Bull. Amer. Math. Soc. (Accepted Paper) 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 G. De Philippis, A. Figalli: Partial Regularity for optimal transport maps Publ. Math. Inst. Hautes Études Sci. (Accepted Paper) 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) 2015 G. De Philippis, A. R. Mészáros, F. Santambrogio, B. Velichkov: BV Estimates in Optimal Transportation and Applications Arch. Ration. Mech. An. (Accepted Paper) 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) 2016 G. De Philippis, A. Figalli: Rigidity and stability of Caffarelli's log-concave perturbation theorem Nonlinear Anal. (Accepted Paper) 2016 L. Brasco, G. De Philippis: Spectral inequalities in quantitative form (Book Chapter) 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) 2016 G. De Philippis, F. Rindler: Characterization of generalized Young measures generated by symmetric gradients Arch. Ration. Mech. An. (Accepted Paper) 2016 G. De Philippis, F. Rindler: On the structure of ${\mathscr A}$-free measures and applications Ann. of Math. (Accepted Paper) 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 G. De Philippis, N. Fusco, A. Pratelli: On the approximation of SBV functions Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 2017 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) 2017 G. De Philippis, F. Rindler: On the structure of measures constrained by linear PDEs (Proceedings) 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) 2017 G. De Philippis, L. Palmieri, F. Rindler: On the two-state problem for general differential operators Nonlinear Anal. (Accepted Paper) 2018 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) 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 G. De Philippis, M. Goldman: A two-point function approach to connectedness of drops in convex potentials CAG (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) 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. Marini, E. Mukoseeva: The sharp quantitative isocapacitary inequality (Submitted Paper) 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) 2019 G. De Philippis, A. Pratelli: The closure of planar diffeomorphisms in Sobolev spaces Ann. Inst. H. Poincaré Anal. Non Linéaire (Accepted Paper) 2019 G. De Philippis, J. Núñez-Zimbrón: The behavior of harmonic functions at singular points of $\mathsf{RCD}$ spaces (preprint) 2019 G. De Philippis, L. Spolaor, B. Velichkov: Regularity of the free boundary for the two-phase Bernoulli problem (Preprint) 2019 G. De Philippis, F. Rindler: Fine properties of functions of bounded deformation -- an approach via linear PDEs (Survey paper) 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 (Accepted Paper) 2019 C. De Lellis, G. De Philippis, J. Hirsch: Nonclassical minimizing surfaces with smooth boundary J. Differential Geom. (Accepted Paper) 2019 G. De Philippis, M. Marini, M. Mazzucchelli, S. Suhr: Closed geodesics on reversible Finsler 2-spheres (Preprint) 2020 G. De Philippis, A. De Rosa, F. Ghiraldin: Existence results for minimizers of parametric elliptic functionals J. Geom. Anal. 2020 L. Brasco, G. De Philippis, G. Franzina: Positive solutions to the sublinear Lane-Emden equation are isolated Comm. Partial Differential Equations (Accepted Paper) p. 31, 2021 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) 2021 G. De Philippis, A. De Rosa: The anisotropic Min-Max theory: Existence of anisotropic minimal and CMC surfaces (Submitted Paper) 2022 G. De Philippis, N. Fusco, M. Morini: Regularity of capillarity droplets with obstacle (Submitted Paper) 2022 G. De Philippis, A. Marchese, A. Merlo, A. Pinamonti, F. Rindler: On the converse of Pansu's theorem (Submitted Paper) 2022