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

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...

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Detalles Bibliográficos
Autores: Carranza, Yino B. Cueva [UNESP], Pimenta, Marcos T. O. [UNESP]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/304399
Acceso en línea:http://dx.doi.org/10.1007/s12215-023-00969-2
https://hdl.handle.net/11449/304399
Access Level:acceso abierto
Palabra clave:1-Laplacian operator
35J62
35J75
Critical nonlinearities
Elliptic systems
Space of functions of bounded variation
Descripción
Sumario: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.