Calculus of Variations and Geometric Measure Theory

T. Schmidt

${\rm W}^{2,1+\varepsilon}$ estimates for the Monge-Ampère equation

created by schmidt on 24 Feb 2012
modified on 17 Apr 2013


Published Paper

Inserted: 24 feb 2012
Last Updated: 17 apr 2013

Journal: Adv. Math.
Volume: 240
Pages: 672-689
Year: 2013
Links: Link to the published version


We study strictly convex Alexandrov solutions $u$ of the real Monge-Ampère equation $\det(\nabla^2u)=f$, where $f$ is measurable, positive, and bounded away from $0$ and $\infty$. Under only these assumptions we prove interior ${\rm W}^{2,1+\varepsilon}$-regularity of $u$.

Tags: GeMeThNES