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

## Schmidt Thomas

published
year: 2013
abstract: 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 $u$.