Accepted Paper
Inserted: 5 feb 2025
Last Updated: 7 jan 2026
Journal: Annales de la Faculté des Sciences de Toulouse (AFST)
Year: 2026
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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