Regularity of solutions to the Dirichlet problem for Monge-Ampère equations

Abstract

We study Hölder continuity of solutions to the Dirichlet problem for measures having density in $L^p$, $p>1$, with respect to Hausdorff-Riesz measures of order $2n-2+\epsilon$ for $0<\epsilon \le 2$, in a bounded strongly hyperconvex Lipschitz domain and the boundary data belongs to $C^{0,\alpha }(\partial \Omega )$, $0<\alpha \le 1$.

14 pages