Global Hölder regularity for the fractional $p$-Laplacian

Antonio Iannizzotto; Sunra J.N. Mosconi; Marco Squassina

doi:10.4171/rmi/921

JournalsrmiVol. 32, No. 4pp. 1353–1392

Global Hölder regularity for the fractional $p$ -Laplacian

Antonio Iannizzotto
Università degli Studi di Cagliari, Italy
- MathSciNet
- zbMATH Open
Sunra J.N. Mosconi
Università degli Studi di Catania, Italy
- MathSciNet
- zbMATH Open
Marco Squassina
Università Cattolica del Sacro Cuore, Brescia, Italy
- MathSciNet
- zbMATH Open

$Global Hölder regularity for the fractional $p$-Laplacian cover$

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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, 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.

Cite this article

Antonio Iannizzotto, Sunra J.N. Mosconi, Marco Squassina, Global Hölder regularity for the fractional $p$ -Laplacian. Rev. Mat. Iberoam. 32 (2016), no. 4, pp. 1353–1392

DOI 10.4171/RMI/921