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Boundary regularity for a degenerate elliptic equation with mixed boundary conditions (1803.10641v1)
Published 28 Mar 2018 in math.AP
Abstract: We consider a function U satisfying a degenerate elliptic equation on (0,+\infty)\times RN with mixed Dirichlet-Neumann boundary conditions. The Neumann condition is prescribed on a bounded domain \Omega\subset RN of class C{1;1}, whereas the Dirichlet data is on the exterior of \Omega. We prove Holder regularity estimates of U/ds, where d is a distance function defined as d(z) := dist(z;RN\setminus\Omega), for z\in (0,+\infty)\times RN. The degenerate elliptic equation arises from the Caffarelli-Silvestre extension of the Dirichlet problem for the fractional Laplacian. Our proof relies on compactness and blow-up analysis arguments.