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Nonlinear Analysis

Asymptotic Expansions of Solutions of the Yamabe Equation and the sigma-k Yamabe Equation near Isolated Singular Points

Qing Han, University of Notre Dame

Location:  Hill 705
Date & time: Tuesday, 26 February 2019 at 1:40PM - 3:00PM

Abstract:  We study asymptotic behaviors of positive solutions to the Yamabe equation and the sigma-k Yamabe equation near isolated singular points and establish expansions up to arbitrary orders. Such results generalize an earlier pioneering work by Caffarelli, Gidas, and Spruck, and a work by Korevaar, Mazzeo, Pacard, and Schoen, on the Yamabe equation, and a work by Han, Li, and Teixeira on the sigma-k Yamabe equation. The proof is based on a study of the linearized operators at radial solutions, following an approach adopted by Korevaar, et al.

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