Boundary regularity for the polyharmonic Dirichlet problem (2502.02964v2)

Published 5 Feb 2025 in math.AP

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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