Boundary regularity for the polyharmonic Dirichlet problem
Analysis of PDEs
2025-02-25 v2
Abstract
In this paper we prove that any solution of the -polyharmonic Poisson equation in a Reifenberg-flat domain with homogeneous Dirichlet boundary condition, is 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.
Cite
@article{arxiv.2502.02964,
title = {Boundary regularity for the polyharmonic Dirichlet problem},
author = {Antoine Lemenant and Rémy Mougenot},
journal= {arXiv preprint arXiv:2502.02964},
year = {2025}
}