Boundary regularity for the polyharmonic Dirichlet problem

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].