Calculus of Variations and Geometric Measure Theory
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G. De Philippis - A. Figalli - O. Savin

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

created by dephilipp on 24 Feb 2012
modified by figalli on 24 Dec 2012


Accepted Paper

Inserted: 24 feb 2012
Last Updated: 24 dec 2012

Journal: Math. Ann.
Year: 2012


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

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


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