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Global Hölder regularity for the fractional $p$-Laplacian (1411.2956v2)
Published 11 Nov 2014 in math.AP
Abstract: By virtue of barrier arguments we prove $C\alpha$-regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional $p$-Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular ($p<2$) of degenerate ($p>2$) case.