On Cusp Solutions to a Prescribed Mean Curvature Equation
  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. 
Alexandra K. Echart and Kirk E. Lancaster
math.AP