Comparison and regularity results for the fractional Laplacian via symmetrization methods

Giuseppina Di Blasio, Bruno Volzone

Published 2011-06-06, updated 2012-01-03Version 4

In this paper we establish a comparison result through symmetrization for solutions to some boundary value problems involving the fractional Laplacian. This allows to get sharp estimates for the solutions, obtained by comparing them with solutions of suitable radial problems. Furthermore, we use such result to prove a priori estimates for solutions in terms of the data, providing several regularity results which extend the well known ones for the classical Laplacian.