Calculus of Variations and Geometric Measure Theory

G. De Philippis - A. Figalli - O. Savin

A note on interior $W^{2,1+\varepsilon}$ estimates for the Monge-Ampere equation

created by dephilipp on 24 Feb 2012
modified on 30 Oct 2017


Accepted Paper

Inserted: 24 feb 2012
Last Updated: 30 oct 2017

Journal: Math. Ann.
Year: 2012

ArXiv: 1202.5566 PDF


By a variant of the techniques introduced by the first two authors in DF to prove that second derivatives of solutions to the Monge-Ampere equation are locally in $L\log L$, we obtain interior $W^{2,1+\varepsilon}$ estimates.

Keywords: Monge-Ampère equation, Sobolev regularity, higher integrability