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

Gonzalo García and Hendel Yaker

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-20

Abstract:

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

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:641294

DOI: 10.1155/IJMMS.2005.679

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