A note on global regularity for the weak solutions of fractional $p$-Laplacian equations

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

doi:10.4171/rlm/719

JournalsrlmVol. 27, No. 1pp. 15–24

A note on global regularity for the weak solutions of fractional $p$ -Laplacian equations

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

$A note on global regularity for the weak solutions of fractional $p$-Laplacian equations cover$

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Abstract

We consider a boundary value problem driven by the fractional $p$ -Laplacian operator with a bounded reaction term. By means of barrier arguments, we prove Hölder regularity up to the boundary for the weak solutions, both in the singular ( $1 < p < 2$ ) and the degenerate ( $p > 2$ ) case.

Cite this article

Antonio Iannizzotto, Sunra J.N. Mosconi, Marco Squassina, A note on global regularity for the weak solutions of fractional $p$ -Laplacian equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 1, pp. 15–24

DOI 10.4171/RLM/719