A Morse Lemma for degenerate critical points of solutions of nonlinear equations in $\R^2$

Massimo Grossi

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arXiv · 1806.08559

A Morse Lemma for degenerate critical points of solutions of nonlinear equations in $\R^2$

Massimo Grossi

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Abstract

In this paper we prove a Morse Lemma for degenerate critical points of a function u which satisfies -\Delta u=f(u) in B_1, where B_1 is the unit ball of R^2 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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Massimo Grossi. 2018-06-22. A Morse Lemma for degenerate critical points of solutions of nonlinear equations in $\R^2$. https://arxiv.org/abs/1806.08559

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