Asymptotic analysis of singular solutions of the scalar and mean curvature equations

We show that positive solutions of a semilinear elliptic problem in the Sobolev critical exponent with Newmann conditions, related to conformal deformation of metrics inR+, are asymptotically symmetric in a neighborhood of the origin. As a consequence, we prove for a related problem of conformal deformation of metrics in R+ that if a solution satisfies a Kazdan-Warner-type identity, then the conformal metric can be realized as a smooth metric on S+.