For operators comparable to the fractional Laplacian of order 2s, solutions with zero exterior data on Reifenberg flat domains are C^{s-ε} up to the boundary.
Boundary regularity for the polyharmonic Dirichlet problem
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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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Boundary regularity for nonlocal elliptic equations over Reifenberg flat domains
For operators comparable to the fractional Laplacian of order 2s, solutions with zero exterior data on Reifenberg flat domains are C^{s-ε} up to the boundary.