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 21 Aug 2012
modified on 15 Jan 2013



Inserted: 21 aug 2012
Last Updated: 15 jan 2013

Year: 2012


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