Existence of ground states and free-boundary problems for the prescribed mean-curvature equation

Abstract

Existence and nonexistence of radially symmetric ground states and compact support solutions for a quasilinear equation involving the mean-curvature operator are studied in dependence of the parameters involved. Different tools are used in the proofs, according to the cases considered. Several numerical results are also given: the experiments show a possible lack of uniqueness of the solution and a strong dependence on the space dimension.