On Cusp Solutions to a Prescribed Mean Curvature Equation

TL;DR

This paper proves the nonexistence of cusp solutions in certain prescribed mean curvature boundary value problems in two-dimensional domains, with implications for radial limits at corners.

Contribution

It establishes conditions under which cusp solutions cannot exist for prescribed mean curvature equations in planar domains.

Findings

Cusp solutions do not exist under certain conditions

Application to radial limits at corners

Provides theoretical nonexistence results

Abstract

The nonexistence of "cusp solutions" of prescribed mean curvature boundary value problems in $\Omega\times{\bf R}$ when $\Omega$ is a domain in ${\bf R}^{2}$ is proven in certain cases and an application to radial limits at a corner is mentioned.