Equivalence of solutions for non-homogeneous p(x)-Laplace equationsy
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...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2023 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/219037 |
| Online Access: | http://hdl.handle.net/11336/219037 |
| Access Level: | Open access |
| Keyword: | COMPARISON PRINCIPLE NONLINEAR ELLIPTIC EQUATIONS P(X)-LAPLACIAN VISCOSITY SOLUTIONS WEAK SOLUTIONS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | 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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