By virtue of barrier arguments we prove Cα-regularity up to the boundary for the weak solutions of a non-local, non-linear 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.
Global Hölder regularity for the fractional p-Laplacian
IANNIZZOTTO, ANTONIO;
2016
Abstract
By virtue of barrier arguments we prove Cα-regularity up to the boundary for the weak solutions of a non-local, non-linear 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.
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