Calculus of Variations and Geometric Measure Theory

A. Lemenant - R. Mougenot

Boundary regularity for the polyharmonic Dirichlet problem

created by lemenant on 05 Feb 2025
modified on 24 Feb 2025

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Inserted: 5 feb 2025
Last Updated: 24 feb 2025

Year: 2025

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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