A Morse Lemma for degenerate critical points of solutions of nonlinear equations in \R²

2018/06/22 by Grossi, Massimo
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.08559

Abstract

In this paper we prove a Morse Lemma for degenerate critical points of a function u which satisfies -Δu=f(u) in B₁, where B₁ is the unit ball of R² and f is a smooth nonlinearity. Other results on the nondegeneracy of the critical points and the shape of the level sets are proved.

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