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...
| Autores: | , |
|---|---|
| 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 |
| 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. |
|---|