Radial Limits of Nonparametric PMC Surfaces with Intermediate Boundary Curvature
We investigate the boundary behavior of the variational solution $f$ of a Dirichlet problem for a prescribed mean curvature equation in a domain $Ω\subset{\bf R}^{2}$ near a point $\mathcal{O}\in\partialΩ$ under different assumptions about the curvature of $\partialΩ$ 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 $ϕ,$ depending on the curvature properties of $\partialΩ$ near $\mathcal{O}.$
math.AP↗