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We prove Holder regularity estimates of U/d^s, where d is a distance function defined as d(z) := dist(z;R^N\\setminus\\Omega), for z\\in (0,+\\infty)\\times R^N. The degenerate elliptic equation arises from the Caffarelli-Silvestre extension of the Dirichlet problem for the fractional Laplacian. 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The Neumann condition is prescribed on a bounded domain \\Omega\\subset R^N of class C^{1;1}, whereas the Dirichlet data is on the exterior of \\Omega. We prove Holder regularity estimates of U/d^s, where d is a distance function defined as d(z) := dist(z;R^N\\setminus\\Omega), for z\\in (0,+\\infty)\\times R^N. The degenerate elliptic equation arises from the Caffarelli-Silvestre extension of the Dirichlet problem for the fractional Laplacian. 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