Energy Stability for a Class of Semilinear Elliptic Problems

被引：2

作者：

Afonso, Danilo Gregorin ^{[1
]}

Iacopetti, Alessandro ^{[2
]}

Pacella, Filomena ^{[1
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Matemat Guido Castelnuovo, Piazzale Aldo Moro 5, I-00185 Rome, Italy

[2] Univ Torino, Dipartimento Matemat G Peano, Via Carlo Alberto 10, I-10123 Turin, Italy

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 03期

关键词：

Semilinear elliptic equations; Variational methods; Stability; Shape optimization in unbounded domains; ISOPERIMETRIC-INEQUALITIES; RADIAL SOLUTIONS; UNIQUENESS;

D O I：

10.1007/s12220-023-01525-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider semilinear elliptic problems in a bounded domain Omega contained in a given unbounded Lipschitz domain C subset of R-N. Our aim is to study how the energy of a solution behaves with respect to volume-preserving variations of the domain Omega inside C. Once a rigorous variational approach to this question is set, we focus on the cases when 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.

引用

页数：43

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