Asymptotic symmetries for conformal scalar curvature equations with singularity

Article

DOI: 10.1007/s00526-005-0002-0

Cite this article as:
Taliaferro, S.D. & Zhang, L. Calc. Var. (2006) 26: 401. doi:10.1007/s00526-005-0002-0

Abstract

We give conditions on a positive Hölder continuous function C2such that every C2 positive solution u((x)) of the conformal scalar curvature equation

\(\Delta u+K(x)u^{\frac{n+2}{n-2}}=0 \)

in a punctured neighborhood of the origin in Rn either has a removable singularity at the origin or satisfies

\(u(x)=u_0(|x|)(1+ {\cal O} (|x|^\beta)) \quad \text{as} \quad |x|\to 0^+\)

for some positive singular solution u0(|x|) of

\(\Delta u_0+K(0)u_0^{\frac{n+2}{n-2}}=0 \quad \text{in}\quad {\bf R}^n\setminus \{0\}\)

where \(\beta\in(0,1)\) is the Hölder exponent of K.Mathematics Subject Classification (2000) Primary 35J60, 53C21

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityTXUSA
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA

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