Equivalence of solutions for non-homogeneous p(x)-Laplace equations
We establish the equivalence between weak and viscosity solutions for non-homogeneous p(x)-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak sol...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/720815 |
| Acceso en línea: | http://hdl.handle.net/10486/720815 https://dx.doi.org/10.3934/mine.2023044 |
| Access Level: | acceso abierto |
| Palabra clave: | Nonlinear elliptic equations p(x)-Laplacian viscosity solutions weak solutions comparison principle Matemáticas |
| Sumario: | We establish the equivalence between weak and viscosity solutions for non-homogeneous p(x)-Laplace equations with a right-hand side term depending on the spatial variable, the unknown, and its gradient. We employ inf- and sup-convolution techniques to state that viscosity solutions are also weak solutions, and comparison principles to prove the converse. The new aspects of the p(x)- Laplacian compared to the constant case are the presence of log-terms and the lack of the invariance under translations |
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