Radial graphs over domains of $\mathbb{S}^{n}$ with prescribed mean   curvature
  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. 
Paolo Caldiroli, Giovanni Gullino
math.DG math.AP