Global Hölder solvability of linear and quasilinear Poisson equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915286544809984 |
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| author | Hara, Takanobu |
| author_facet | Hara, Takanobu |
| contents | We establish an existence result for globally continuous weak solutions to elliptic equations of the $p$-Poisson type. This result significantly improves Theorem 8.30 in Gilbarg-Trudinger (1983) and offers a novel contribution for the classical Poisson equation on Lipschitz domains, ensuring global Hölder continuity of solutions under a minimal assumption on the right-hand side. Applications of this result to embedding theorems are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global Hölder solvability of linear and quasilinear Poisson equations Hara, Takanobu Analysis of PDEs Functional Analysis 35J92, 35J25, 31C45 We establish an existence result for globally continuous weak solutions to elliptic equations of the $p$-Poisson type. This result significantly improves Theorem 8.30 in Gilbarg-Trudinger (1983) and offers a novel contribution for the classical Poisson equation on Lipschitz domains, ensuring global Hölder continuity of solutions under a minimal assumption on the right-hand side. Applications of this result to embedding theorems are also discussed. |
| title | Global Hölder solvability of linear and quasilinear Poisson equations |
| topic | Analysis of PDEs Functional Analysis 35J92, 35J25, 31C45 |
| url | https://arxiv.org/abs/2311.09701 |