On a higher-integrability estimate for Laplacians of convex solutions to the Monge-Ampère equation

Diego Maldonado

A maximum principle for certain strictly convex functions belonging to $W_{\mathrm{loc}}^{2,1}(\Omega )\cap C^1(\Omega )$ is established and then applied to obtain a $W^{2,1 +\eps}_{\rm loc}(Ω)$-es…