The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions

We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation−div(∇u/1+|∇u|2)=−au+b/1+|∇u|2, where a,b>0a,b>0 are given parameters and Ω is a bounded Lipschitz domain in RNRN. This equation appears in the modeling theory of capillarity phenomena for compressible fluids and in the description of the geometry of the human cornea.