In this paper we construct families of bounded domains Ωε and solutions uε of ( −∆uε = 1 in Ωε uε = 0 on ∂Ωε such that, for any integer k ≥ 2, uε admits at least k maximum points for small enough . The domain Ωε is “not far” to be convex in the sense that it is starshaped, the curvature of ∂Ωε vanishes at exactly two points and the minimum of the curvature of ∂Ωε goes to 0 as ε → 0

On the number of critical points of solutions of semilinear equations in R^2 / Gladiali, Francesca; Grossi, Massimo. - In: AMERICAN JOURNAL OF MATHEMATICS. - ISSN 0002-9327. - (2022). [10.1353/ajm.2022.0028]

On the number of critical points of solutions of semilinear equations in R^2

Massimo Grossi
2022

Abstract

In this paper we construct families of bounded domains Ωε and solutions uε of ( −∆uε = 1 in Ωε uε = 0 on ∂Ωε such that, for any integer k ≥ 2, uε admits at least k maximum points for small enough . The domain Ωε is “not far” to be convex in the sense that it is starshaped, the curvature of ∂Ωε vanishes at exactly two points and the minimum of the curvature of ∂Ωε goes to 0 as ε → 0
2022
punti critici, problema della torsione, curvatura
01 Pubblicazione su rivista::01a Articolo in rivista
On the number of critical points of solutions of semilinear equations in R^2 / Gladiali, Francesca; Grossi, Massimo. - In: AMERICAN JOURNAL OF MATHEMATICS. - ISSN 0002-9327. - (2022). [10.1353/ajm.2022.0028]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1637947
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