JournalsrlmVol. 22, No. 3pp. 311–336

Regularity of optimal transport maps and partial differential inclusions

  • Luigi Ambrosio

    Scuola Normale Superiore, Pisa, Italy
  • Guido De Philippis

    Scuola Normale Superiore, Pisa, Italy
  • Bernd Kirchheim

    Universität Leipzig, Germany
Regularity of optimal transport maps and partial differential inclusions cover
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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