Uniqueness of the critical point for semi-stable solution in\n \ℝ²

2020/04/23 by Fabio De Regibus, Massimo Grossi, De Regibus, Fabio +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.11330

openalex publication_date 2020/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show the uniqueness of the critical point for\n\semi-stable solutions of the problem
begincases -
Deltaν=f(u)amp;
textin
Omega

ugt;0amp;
textin
Omega

u=0amp;
texton \n
partial
Omega,
endcases where \Ω\⊂\ℝ² is a smooth\nbounded domain whose boundary has \nonnegative curvature and f(0)\≥0.\nIt extends a result by Cabr 'e-Chanillo to the case where the curvature of\n\∂\Ω vanishes.\n

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