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arXiv · 2502.02964

Boundary regularity for the polyharmonic Dirichlet problem

Antoine Lemenant·Rémy Mougenot
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Abstract

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 $\mathscr{C}^{m-1,\alpha}$ 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.

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Antoine Lemenant, Rémy Mougenot. 2025-02-05. Boundary regularity for the polyharmonic Dirichlet problem. https://arxiv.org/abs/2502.02964

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