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.
2019
Elliptic equations, level sets, morse theory
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1357757
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