Radial Limits of Nonparametric PMC Surfaces with Intermediate Boundary Curvature

Abstract

We investigate the boundary behavior of the variational solution $f$ of a Dirichlet problem for a prescribed mean curvature equation in a domain $\Omega \subset {\mathbf{R}}^2$ near a point $\mathcal{O}\in \partial \Omega$ under different assumptions about the curvature of $\partial \Omega$ on each side of $\mathcal{O}.$ We prove that the radial limits at $\mathcal{O}$ of $f$ exist under different assumptions about the Dirichlet boundary data $\varphi ,$ depending on the curvature properties of $\partial \Omega$ near $\mathcal{O}.$