International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 5, Pages 679-698
doi:10.1155/IJMMS.2005.679
Asymptotic analysis of singular solutions of the scalar and mean curvature equations
1Departamento de Matemáticas, Facultad de Ciencias, Universidad del Valle, Cali, Colombia
2Departamento de Matemáticas y Estadística, Facultad de Ingeniería, Universidad Icesi, Cali, Colombia
Received 21 October 2003; Revised 18 January 2005
Copyright © 2005 Gonzalo García and Hendel Yaker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 ℝ+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 ℝ+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.