SU\G(𝔾)/K·U

Boundary regularity for the polyharmonic Dirichlet problem

Antoine Lemenant, RĂ©my Mougenot

Type: Preprint

Publication Date: 2025-02-05

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2502.02964

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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  • arXiv (Cornell University) - View - PDF

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