Work

Boundary regularity for the polyharmonic Dirichlet problem

Year: 2026

Type: article

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 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 [12].

Source: Annales de la faculté des sciences de Toulouse Mathématiques

DOI: 10.5802/afst.1862

Authors: Antoine Lemenant, Rémy Mougenot

Institutions: Centre National de la Recherche Scientifique, Institut Élie Cartan de Lorraine, Université de Lorraine

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4407212953

FWCI:

Cites:

Cited by: 1

Related to: 10