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

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  • Gonzalo García
  • Hendel Yaker

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 .

Suggested Citation

  • Gonzalo García & Hendel Yaker, 2005. "Asymptotic analysis of singular solutions of the scalar and mean curvature equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-20, January.
    • Handle: RePEc:hin:jijmms:641294
    DOI: 10.1155/IJMMS.2005.679
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