Regularity for the prescribed vertical mean curvature system in the plane

Abstract

We prove everywhere regularity for Lipschitz solutions to the prescribed vertical mean curvature system in the plane, where the codimension is arbitrary and the mean curvature is in $L^r, \, r > 2$. This strengthens and extends our previous result on the Lawson-Osserman conjecture, https://arxiv.org/abs/2308.04997.