In this paper we show the uniqueness of the critical point for semi-stable solutions of the problem {-Δu=f(u)inΩu>0inΩu=0on∂Ω,where Ω ⊂ R2 is a smooth bounded domain whose boundary has nonnegative curvature and f(0) ≥ 0. It extends a result by Cabré-Chanillo to the case where the curvature of ∂Ω vanishes.
Uniqueness of the critical point for semi-stable solutions in R2 / De Regibus, F.; Grossi, M.; Mukherjee, D.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 60:1(2021). [10.1007/s00526-020-01903-5]
Uniqueness of the critical point for semi-stable solutions in R2
De Regibus F.;Grossi M.
;
2021
Abstract
In this paper we show the uniqueness of the critical point for semi-stable solutions of the problem {-Δu=f(u)inΩu>0inΩu=0on∂Ω,where Ω ⊂ R2 is a smooth bounded domain whose boundary has nonnegative curvature and f(0) ≥ 0. It extends a result by Cabré-Chanillo to the case where the curvature of ∂Ω vanishes.File allegati a questo prodotto
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