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.
Fractional p-Laplacian, Fractional Sobolev spaces, Global Hölder regularity
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/186809
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