In this paper we prove a Morse Lemma for degenerate critical points of a function u which satisfies - Δ u = f (u) in B1, where u ∈ C2 (B1), 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.
A Morse Lemma for Degenerate Critical Points of Solutions of Nonlinear Equations in R 2 / Grossi, M.. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - 20:1(2019), pp. 1-18. [10.1515/ans-2019-2055]
A Morse Lemma for Degenerate Critical Points of Solutions of Nonlinear Equations in R 2
Grossi M.
2019
Abstract
In this paper we prove a Morse Lemma for degenerate critical points of a function u which satisfies - Δ u = f (u) in B1, where u ∈ C2 (B1), 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.File allegati a questo prodotto
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