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1

Higher Integrability for Minimizers of the Mumford–Shah Functional

De Philippis, Guido, Figalli, Alessio

Journal:

Archive for Rational Mechanics and Analysis

Year:

2014

Language:

english

File:

PDF, 178 KB

english, 2014

2

Faber–Krahn inequalities in sharp quantitative form

Brasco, Lorenzo, De Philippis, Guido, Velichkov, Bozhidar

Journal:

Duke Mathematical Journal

Year:

2015

Language:

english

File:

PDF, 706 KB

english, 2015

3

Second order stability for the Monge–Ampère equation and strong Sobolev convergence of optimal transport maps

De Philippis, Guido, Figalli, Alessio

Journal:

Year:

2013

Language:

english

File:

PDF, 492 KB

english, 2013

4

Partial regularity for optimal transport maps

De Philippis, Guido, Figalli, Alessio

Journal:

Publications Mathématiques de L'IHÉS

Year:

2015

Language:

english

File:

PDF, 458 KB

english, 2015

5

W2,1regularity for solutions of the Monge–Ampère equation

De Philippis, Guido, Figalli, Alessio

Journal:

Inventiones mathematicae

Year:

2013

Language:

english

File:

PDF, 558 KB

english, 2013

6

Optimal regularity of the convex envelope

De Philippis, Guido, Figalli, Alessio

Journal:

Transactions of the American Mathematical Society

Year:

2014

Language:

english

File:

PDF, 257 KB

english, 2014

7

Rigidity and stability of Caffarelli’s log-concave perturbation theorem

De Philippis, Guido, Figalli, Alessio

Journal:

Nonlinear Analysis: Theory, Methods & Applications

Year:

2016

Language:

english

File:

PDF, 722 KB

english, 2016

8

Dimensional estimates for singular sets in geometric variational problems with free boundaries

De Philippis, Guido, Maggi, Francesco

Journal:

Journal für die reine und angewandte Mathematik (Crelles Journal)

Year:

2017

Language:

english

File:

PDF, 417 KB

english, 2017

9

On the Aleksandrov–Bakelman–Pucci estimate for the infinity Laplacian

Fernando Charro, Guido De Philippis…

Journal:

Calculus of Variations and Partial Differential Equations

Year:

2013

Language:

english

File:

PDF, 346 KB

english, 2013

10

Spectral optimization for the Stekloff–Laplacian: The stability issue

Lorenzo Brasco, Guido De Philippis, Berardo Ruffini

Journal:

Journal of Functional Analysis

Year:

2012

Language:

english

File:

PDF, 324 KB

english, 2012

11

BV Estimates in Optimal Transportation and Applications

De Philippis, Guido, Mészáros, Alpár Richárd, Santambrogio, Filippo, Velichkov, Bozhidar

Journal:

Archive for Rational Mechanics and Analysis

Year:

2016

Language:

english

File:

PDF, 646 KB

english, 2016

12

Essential connectedness and the rigidity problem for Gaussian symmetrization

Cagnetti, Filippo, Colombo, Maria, De Philippis, Guido, Maggi, Francesco

Journal:

Journal of the European Mathematical Society

Year:

2017

Language:

english

File:

PDF, 318 KB

english, 2017

13

Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness

Crasta, Graziano, De Cicco, Virginia, De Philippis, Guido, Ghiraldin, Francesco

Journal:

Archive for Rational Mechanics and Analysis

Year:

2016

Language:

english

File:

PDF, 598 KB

english, 2016

14

Dimensional estimates and rectifiability for measures satisfying linear PDE constraints

Arroyo-Rabasa, Adolfo, De Philippis, Guido, Hirsch, Jonas, Rindler, Filip

Journal:

Geometric And Functional Analysis

Year:

2019

Language:

english

File:

PDF, 380 KB

english, 2019

15

Gamma-convergence of nonlocal perimeter functionals

Luigi Ambrosio, Guido De Philippis, Luca Martinazzi

Journal:

manuscripta mathematica

Year:

2011

Language:

english

File:

PDF, 281 KB

english, 2011

16

Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case

Ambrosio, Luigi, Colombo, Maria, De Philippis, Guido, Figalli, Alessio

Journal:

Communications in Partial Differential Equations

Year:

2012

Language:

english

File:

PDF, 207 KB

english, 2012

17

From volume cone to metric cone in the nonsmooth setting

De Philippis, Guido, Gigli, Nicola

Journal:

Geometric And Functional Analysis

Year:

2016

Language:

english

File:

PDF, 1.00 MB

english, 2016

18

Sobolev Regularity for Monge-Ampère Type Equations

De Philippis, Guido, Figalli, Alessio

Journal:

SIAM Journal on Mathematical Analysis

Year:

2013

Language:

english

File:

PDF, 221 KB

english, 2013

19

Weak notions of Jacobian determinant and relaxation

De Philippis, Guido

Journal:

ESAIM Control Optimisation and Calculus of Variations

Year:

2012

Language:

english

File:

PDF, 360 KB

english, 2012

20

Regularity of optimal transport maps and partial differential inclusions

Ambrosio, Luigi, De Philippis, Guido, Kirchheim, Bernd

Journal:

Rendiconti Lincei - Matematica e Applicazioni

Year:

2011

Language:

english

File:

PDF, 190 KB

english, 2011

21

Characterization of Generalized Young Measures Generated by Symmetric Gradients

De Philippis, Guido, Rindler, Filip

Journal:

Archive for Rational Mechanics and Analysis

Year:

2017

Language:

english

File:

PDF, 739 KB

english, 2017

22

Regularity of minimizers of shape optimization problems involving perimeter

De Philippis, Guido, Lamboley, Jimmy, Pierre, Michel, Velichkov, Bozhidar

Journal:

Journal de Mathématiques Pures et Appliquées

Year:

2017

Language:

english

File:

PDF, 562 KB

english, 2017

23

A note on Petty's theorem

Marini, Michele, de Philippis, Guido

Journal:

Kodai Mathematical Journal

Year:

2014

Language:

english

File:

PDF, 96 KB

english, 2014

24

Partial Differential Equations

De Philippis, Guido, Schoen, Richard, Topping, Peter

Journal:

Oberwolfach Reports

Year:

2020

File:

PDF, 880 KB

2020

25

Regularity of optimal transport maps and partial differential inclusions

Ambrosio, Luigi, De Philippis, Guido, Kirchheim, Bernd

Journal:

Rendiconti Lincei - Matematica e Applicazioni

Year:

2011

File:

PDF, 190 KB

2011

26

Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints

Arroyo-Rabasa, Adolfo, De Philippis, Guido, Rindler, Filip

Journal:

Advances in Calculus of Variations

Year:

2018

Language:

english

File:

PDF, 988 KB

english, 2018

27

Regularity of Optimal Transport Maps and Applications || Second order stability for the Monge-Ampère equation and applications

De Philippis, Guido

Year:

2013

Language:

english

File:

PDF, 316 KB

english, 2013

28

Rectifiability of Varifolds with Locally Bounded First Variation with Respect to Anisotropic Surface Energies

De Philippis, Guido, De Rosa, Antonio, Ghiraldin, Francesco

Journal:

Communications on Pure and Applied Mathematics

Year:

2017

Language:

english

File:

PDF, 289 KB

english, 2017

29

Regularity of Optimal Transport Maps and Applications ||

De Philippis, Guido

Year:

2013

Language:

english

File:

PDF, 1.26 MB

english, 2013

30

Kinetic Formulation and Uniqueness for Scalar Conservation Laws with Discontinuous Flux

Crasta, Graziano, De Cicco, Virginia, De Philippis, Guido

Journal:

Communications in Partial Differential Equations

Year:

2015

Language:

english

File:

PDF, 289 KB

english, 2015

31

On the two-state problem for general differential operators

De Philippis, Guido, Palmieri, Luca, Rindler, Filip

Journal:

Nonlinear Analysis: Theory, Methods & Applications

Year:

2018

Language:

english

File:

PDF, 687 KB

english, 2018

32

Existence of Isoperimetric Sets with Densities “Converging from Below” on\({\mathbb {R}}^N\)

De Philippis, Guido, Franzina, Giovanni, Pratelli, Aldo

Journal:

Journal of Geometric Analysis

Year:

2017

Language:

english

File:

PDF, 519 KB

english, 2017

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