On the Neumann problem with the Hardy-Sobolev potential (Q2462190)

This paper deals with the qualitative analysis of a nonlinear Neumann problem with indefinite weight function. The main feature of this work consists in the lack of compactness, namely the presence of a critical Hardy-Sobolev nonlinearity. The author investigates the common effect of the shape of the graph of a weight function and the mean curvature of the boundary on the existence of solutions. A particular interest is given to the optimal regularity of solutions. The proofs rely on variational methods combined with refined elliptic estimates and asymptotic analysis.