The Dirichlet problem for a class of prescribed curvature equations

Abstract

In this paper, we consider the Dirichlet problem for a class of prescribed curvature equations. Both degenerate and non-degenerate cases are considered. The existence of the $C^{1,1}$ regular graphic hypersurfaces with prescribing a class of curvatures and constant boundary is proved for the degenerate case.

arXiv commentIn this version, we improve our results to the degenerate case. Furthermore, the conditions on the domain are weakened