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
L. Brasco, G. De Philippis, B. Ruffini:
Spectral optimization for the Stekloff--Laplacian: the stability issue
J. Funct. Anal. (Accepted Paper) p. 28, 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
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
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, 2015
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. 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. 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, A. De Rosa, F. Ghiraldin:
Rectifiability of varifolds with locally bounded first variation with respect to anisotropic surface energies
Comm. Pure App. Math. 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. Pratelli:
The closure of planar diffeomorphisms in Sobolev spaces
(Preprint) 2017
G. De Philippis, N. Gigli:
Non-collapsed spaces with Ricci curvature bounded from below
(Preprint) 2017
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
G. De Philippis, A. De Rosa, F. Ghiraldin:
Existence results for minimizers of parametric elliptic functionals
J. Geom. Anal. 2017
G. De Philippis, L. Palmieri, F. Rindler:
On the two-state problem for general differential operators
Nonlinear Anal. (Accepted Paper) 2018
G. De Philippis, T. Laux:
Implicit time discretization for the mean curvature flow of outward minimizing sets
(Preprint) 2018
C. De Lellis, G. De Philippis, J. Hirsch, A. Massaccesi:
Boundary regularity of mass-minimizing integral currents and a question of Almgren
To appear in the Matrix Annals (Accepted Paper) 2018
G. De Philippis, M. Goldman:
A two-point function approach to connectedness of drops in convex potentials
(Preprint) 2018
C. De Lellis, G. De Philippis, J. Hirsch, A. Massaccesi:
On the boundary behavior of mass-minimizing integral currents
(Preprint) 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, J. Hirsch, G. Vescovo:
Regularity of minimizers for a model of charged droplets
(Submitted Paper) 2019
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