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Energy stability for a class of semilinear elliptic problems
Authors
Danilo Gregorin Afonso
Alessandro Iacopetti
Filomena Pacella
Publication date
14 July 2023
Publisher
View
on
arXiv
Abstract
In this paper, we consider semilinear elliptic problems in a bounded domain
Ω
\Omega
Ω
contained in a given unbounded Lipschitz domain
C
⊂
R
N
\mathcal C \subset \mathbb R^N
C
⊂
R
N
. Our aim is to study how the energy of a solution behaves with respect to volume-preserving variations of the domain
Ω
\Omega
Ω
inside
C
\mathcal C
C
. Once a rigorous variational approach to this question is set, we focus on the cases when
C
\mathcal C
C
is a cone or a cylinder and we consider spherical sectors and radial solutions or bounded cylinders and special one-dimensional solutions, respectively. In these cases, we show both stability and instability results, which have connections with related overdetermined problems.Comment: 33 page
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oai:arXiv.org:2307.07345
Last time updated on 20/07/2023