Boundary behavior near reentrant corners for solutions of certain elliptic equations

The behavior near a reentrant corner of quasilinear non-uniformly elliptic partial differential equations which satisfy certain conditions is examined. For an elliptic equation satisfying a general maximum principle and having «convex barriers», we show that if a solution has radial limits at the corner, these limits have the same qualitative behavior as those for nonparametric minimal surfaces. For certain equations of mean curvature type, radial limits at the reentrant corner are shown to exist.