Boundary regularity for the Poisson equation in reifenberg-flat domains

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This paper is devoted to the investigation of the boundary regularity for the Poisson equation cc -Δu = f & in Ω u= 0 & on ∂ Ω where f belongs to some Lᵖ(Ω) and Ω is a Reifenberg-flat domain of Rⁿ. More precisely, we prove that given an exponent α∈ (0,1), there exists an ε>0 such that the solution u to the previous system is locally Hölder continuous provided that Ω is (ε,r₀)-Reifenberg-flat. The proof is based on Alt-Caffarelli-Friedman's monotonicity formula and Morrey-Campanato theorem.