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arXiv · 1411.2956

Global Hölder regularity for the fractional $p$-Laplacian

Antonio Iannizzotto·Sunra Mosconi·Marco Squassina
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Abstract

By virtue of barrier arguments we prove $C^α$-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.

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Antonio Iannizzotto, Sunra Mosconi, Marco Squassina. 2015-10-26. Global Hölder regularity for the fractional $p$-Laplacian. https://arxiv.org/abs/1411.2956

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