# Boundary Continuity of Nonparametric Prescribed Mean Curvature Surfaces

## TL;DR

This paper studies the boundary behavior of solutions to prescribed mean curvature equations, showing that under certain curvature conditions and boundary data continuity, solutions are continuous at specific boundary points.

## Contribution

It establishes the boundary continuity of variational solutions at smooth points with curvature conditions, even without local barrier functions.

## Key findings

- Solutions are continuous at boundary points with specific curvature conditions when boundary data is continuous.
- Boundary behavior is characterized without relying on local barrier functions.
- Provides conditions ensuring boundary regularity of prescribed mean curvature surfaces.

## Abstract

We investigate the boundary behavior of variational solutions of Dirichlet problems for prescribed mean curvature equations at smooth boundary points where certain boundary curvature conditions are satisfied (which preclude the existence of local barrier functions). We prove that if the Dirichlet boundary data $\phi$ is continuous at such a point (and possibly nowhere else), then the solution of the variational problem is continuous at this point.