Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916288788430848 |
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| author | Mengesha, Tadele Otarola, Enrique Salgado, Abner J. |
| author_facet | Mengesha, Tadele Otarola, Enrique Salgado, Abner J. |
| contents | We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is assumed that the weights belong to the Muckenhoupt class $A_p$ with $p \in (1,\infty$). We also propose and analyze a convergent finite element discretization for the nonlinear elliptic boundary value problems mentioned above. As an instrumental result, we prove that the discretization of certain linear problems are well posed in weighted spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10762 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes Mengesha, Tadele Otarola, Enrique Salgado, Abner J. Analysis of PDEs Numerical Analysis 35A01, 35A02, 35B45, 35J57, 35J60, 65N12, 65N30 We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is assumed that the weights belong to the Muckenhoupt class $A_p$ with $p \in (1,\infty$). We also propose and analyze a convergent finite element discretization for the nonlinear elliptic boundary value problems mentioned above. As an instrumental result, we prove that the discretization of certain linear problems are well posed in weighted spaces. |
| title | Analysis and approximation of elliptic problems with Uhlenbeck structure in convex polytopes |
| topic | Analysis of PDEs Numerical Analysis 35A01, 35A02, 35B45, 35J57, 35J60, 65N12, 65N30 |
| url | https://arxiv.org/abs/2406.10762 |