Quasilinear elliptic systems involving the 1-Laplacian operator with subcritical and critical nonlinearities

被引：0

作者：

Carranza, Yino B. Cueva ^{[1
]}

Pimenta, Marcos T. O. ^{[2
]}

机构：

[1] Univ Estadual Paulista Unesp, Dept Matemat, Intituto Biociencias Letras & Ciencias Exatas, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

[2] Univ Estadual Paulista Unesp, Fac Ciencias & Tecnol, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP, Brazil

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2024年 / 73卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

Elliptic systems; 1-Laplacian operator; Space of functions of bounded variation; Critical nonlinearities;

D O I：

10.1007/s12215-023-00969-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study some systems of elliptic PDEs involving the 1-Laplacian operator. In the first one, we deal with the subcritical regime, while in the second, we study a system with nonlinearities with critical growth. The approach is based on an approximation argument, in which the solutions are obtained as the limit of related problems with the p-Laplacian operator. In order to overcome the lack of compactness in the critical case, a version of the Concentration of Compactness Principle of Lions is proved.

引用

页码：1037 / 1058

页数：22

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