Asymptotic behavior of solutions to the σk-Yamabe equation near isolated singularities
By Zheng-chao Han, Yanyan Li, E. Teixeira. 2009
73 citations recorded by the source corpus.
Abstractσk-Yamabe equations are conformally invariant equations generalizing the classical Yamabe equation. In (J. Funct. Anal. 233: 380–425, 2006) YanYan Li proved that an admissible solution with an isolated singularity at 0∈ℝn to the σk-Yamabe equation is asymptotically radially symmetric. In this work we prove that such a solution is asymptotic to a radial solution to the same equation on ℝn∖{0}. These results generalize earlier pioneering work in this direction on the classical Yamabe equation by Caffarelli, Gidas, and Spruck. In extending the work of Caffarelli et al., we formulate and prove a general asymptotic approximation result for solutions to certain ODEs which include the case for scalar curvature and σk curvature cases. An alternative proof is also provided using analysis of the linearized operators at the radial solutions, along the lines of approach in a work by Korevaar, Mazzeo, Pacard, and Schoen.
View Paper: https://www.semanticscholar.org/paper/7efa9f779f70b6086ec6a2d8e49034228b1388af
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Citations in the corpus
- Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities (2019, unknown): “The main theorems of [5] and [28] were completely extended to solutions of second order fully nonlinear Yamabe equations by Li-Li [30], Y.Y. Li [31], Chang-Han-Yang [10] and Han-Li-Teixeira [23].”
- Asymptotic Expansions of Solutions of the Yamabe Equation and the σk‐Yamabe Equation near Isolated Singular Points (2019, methodology): “Based on earlier results by Li [12], Han, Li, and Teixeira [10] proved the following results for the σk-Yamabe equation (1.”