Radial graphs over domains of ${\mathbb{S}}^n$ with prescribed mean curvature

Abstract

We prove the existence and uniqueness of radial graphs over a given domain of ${\mathbb{S}}^n$ having boundary on the sphere ${\mathbb{S}}^n$ and whose mean curvature at every point equals a prescribed positive function satisfying suitable barrier-type and monotonicity conditions.

12 pages, accepted for publication in Journal of Fixed Point Theory and Applications