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

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.

7 pages, Conferenza tenuta al XXV Convegno Nazionale di Calcolo delle Variazioni, Levico 2--6 febbraio 2015