On the fractional relativistic Schrödinger operator

Abstract

We collect some interesting results for equations driven by the fractional relativistic Schrödinger operator (−Δ+m2)s with s∈(0,1) and m>0. More precisely, for the linear theory, we prove Hölder-Schauder-Zygmund regularity results and a Kato's inequality. For the nonlinear theory, we obtain L∞-regularity, exponential decay, a Pohozaev-type identity, and a symmetry result for solutions of certain nonlinear fractional problems.