Lorentz-regularity for the fractional Poisson problem with \(L^1\)-data

In this talk, I focus on the regularity of so-called very weak solutions to the Poisson Problem for the linear fractional Laplacian on a bounded domain and equipped with homogeneous Dirichlet boundary conditions. I will recall known results and show you how one can could improve these results by using classical symmetrization techniques.

This is joint work with Barbara Brandolini (University of Palermo, Italy) and Vincenzo Ferone (university of Naples, Federico II, Italy)