Boundary regularity for the polyharmonic Dirichlet problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909507607592960 |
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| author | Lemenant, Antoine Mougenot, Rémy |
| author_facet | Lemenant, Antoine Mougenot, Rémy |
| contents | In this paper we prove that any solution of the $m$-polyharmonic Poisson equation in a Reifenberg-flat domain with homogeneous Dirichlet boundary condition, is $\mathscr{C}^{m-1,α}$ regular up to the boundary. To achieve this result we extend the Nirenberg method of translations to operators of arbitrary order, and then use some Mosco-convergence tools developped in a previous paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02964 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary regularity for the polyharmonic Dirichlet problem Lemenant, Antoine Mougenot, Rémy Analysis of PDEs In this paper we prove that any solution of the $m$-polyharmonic Poisson equation in a Reifenberg-flat domain with homogeneous Dirichlet boundary condition, is $\mathscr{C}^{m-1,α}$ regular up to the boundary. To achieve this result we extend the Nirenberg method of translations to operators of arbitrary order, and then use some Mosco-convergence tools developped in a previous paper. |
| title | Boundary regularity for the polyharmonic Dirichlet problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.02964 |