Comparison and regularity results for the fractional Laplacian via symmetrization methods

2011/06/06 by Giuseppina Di Blasio, Di Blasio, Giuseppina, Bruno Volzone +1
Mathematics · #15A15 #35B45 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:15A15 #msc:35B45 #msc:35R11

paper · pdf · doi:10.48550/arxiv.1106.0997

23 pages, 1 figure

arxiv created 2012/01/03 · arxiv updated 2012/01/04

Abstract

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.

Related

• Symmetrization for fractional nonlinear elliptic problems
• Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application
• Symmetrization for fractional Neumann problems
• Variety of fractional Laplacians
• Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data