Regularity of optimal transport maps and partial differential inclusions

Luigi Ambrosio; Guido De Philippis; Bernd Kirchheim

doi:10.4171/rlm/602

JournalsrlmVol. 22, No. 3pp. 311–336

Regularity of optimal transport maps and partial differential inclusions

Luigi Ambrosio
Scuola Normale Superiore, Pisa, Italy
- MathSciNet
- zbMATH Open
Guido De Philippis
Scuola Normale Superiore, Pisa, Italy
Bernd Kirchheim
Universität Leipzig, Germany
- MathSciNet
- zbMATH Open

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Abstract

In this work we address the issue of Sobolev regularity of solutions of Monge-Ampere equations in a borderline case and show how this question is related to a rigidity problem for partial di¤erential inclusions.

Cite this article

Luigi Ambrosio, Guido De Philippis, Bernd Kirchheim, Regularity of optimal transport maps and partial differential inclusions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 3, pp. 311–336

DOI 10.4171/RLM/602