Boundary regularity for the polyharmonic Dirichlet problem

Fuente: arXiv
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Hauptverfasser: Lemenant, Antoine, Mougenot, Rémy
Format: Preprint
Veröffentlicht: 2025
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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