Calculus of Variations and Geometric Measure Theory

A. Figalli

Sobolev regularity for the Monge-Ampère equation, with application to the semigeostrophic equations

created by figalli on 13 Aug 2024

[BibTeX]

Published Paper

Inserted: 13 aug 2024
Last Updated: 13 aug 2024

Journal: J. Math. Sci. (N.Y.)
Year: 2014

Abstract:

In this note we review some recent results on the Sobolev regularity of solutions to the Monge-Ampère equation, and show how these estimates can be used to prove some global existence results for the semi-geostrophic equations.


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