Heat content estimates for the fractional Schrödinger operator $(-\Delta {)}^{\frac{\alpha }{2}}+c{1}_{\Omega },c>0$

Abstract

This paper establishes by employing analytic and probabilistic techniques estimates concerning the heat content for the fractional Schrödinger operator $(-\Delta {)}^{\frac{\alpha }{2}}+c{1}_{\Omega },c>0$ with $0<\alpha \le 2$ in ${\mathbb{R}}^d$, $d\ge 2$ and $\Omega$ a Lebesgue measure set satisfying some regularity conditions.