Revista Matemática Iberoamericana

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Volume 32, Issue 4, 2016, pp. 1353–1392
DOI: 10.4171/RMI/921

Published online: 2016-12-16

Global Hölder regularity for the fractional $p$-Laplacian

Antonio Iannizzotto[1], Sunra J.N. Mosconi[2] and Marco Squassina[3]

(1) Università degli Studi di Cagliari, Italy
(2) Università degli Studi di Catania, Italy
(3) Università Cattolica del Sacro Cuore, Brescia, Italy

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

Keywords: Fractional $p$-Laplacian, fractional Sobolev spaces, global Hölder regularity

Iannizzotto Antonio, Mosconi Sunra, Squassina Marco: Global Hölder regularity for the fractional $p$-Laplacian. Rev. Mat. Iberoamericana 32 (2016), 1353-1392. doi: 10.4171/RMI/921