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.