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
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
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. Goldman:
A two-point function approach to connectedness of drops in convex
potentials
CAG (Accepted Paper) 2018
G. De Philippis, L. Palmieri, F. Rindler:
On the two-state problem for general differential operators
Nonlinear Anal. (Accepted Paper) 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
C. De Lellis, G. De Philippis, J. Hirsch:
Nonclassical minimizing surfaces with smooth boundary
J. Differential Geom. (Accepted 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 2019
G. De Philippis, F. Rindler:
Fine properties of functions of bounded deformation -- an approach via
linear PDEs
(Survey 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
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
L. De Masi, G. De Philippis:
Min-max construction of minimal surfaces with a fixed angle at the
boundary
(preprint) 2021
A. Arroyo-Rabasa, G. De Philippis, J. Hirsch, F. Rindler, A. Skorobogatova:
Higher integrability for measures satisfying a PDE constraint
(preprint) 2021
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, L. Spolaor, B. Velichkov:
Regularity of the free boundary for the two-phase Bernoulli problem
Inventiones mathematicae 2021
G. De Philippis, L. Spolaor, B. Velichkov:
(Quasi-)conformal methods in two-dimensional free boundary problems
J. Eur. Math. Soc. (Accepted Paper) 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) 2022
G. De Philippis, A. Marchese, A. Merlo, A. Pinamonti, F. Rindler:
On the converse of Pansu's Theorem
(Submitted Paper) 2022
G. De Philippis, M. Goldman, B. Ruffini:
From energy bounds to dimensional estimates in a branched transport model for type-I superconductors
(Submitted Paper) 2023
G. De Philippis, R. Tione:
On singular strictly convex solutions to the Monge-Ampere equation
(Preprint) 2023
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, A. Guerra, R. Tione:
Unique continuation for differential inclusions
(preprint) 2023
G. De Philippis, C. Gasparetto, F. Schulze:
A short proof of Allards and Brakkes regularity theorems
International Mathematics Research Notices 2023