The Neumann problem for semilinear elliptic equations with critical Sobolev exponent
This paper is mainly devoted to the study of least energy solutions of a nonlinear elliptic equation with critical Sobolev exponent and Neumann boundary condition. The existence of solutions is deduced with topological linking arguments combined with sharp Sobolev inequalities. This result is then extended to singular potentials by means of the Hardy-Sobolev inequality. Related regularity properties of solutions are also established in the present paper.
scientific article; zbMATH DE number 5292360