Estimates concerning the heat content for the Schrödinger operator related to a subordinate Brownian motion

Abstract

In this paper, we study the heat content for the Schrödinger operator related to a subordinate Brownian motion and we also establish its small time asymptotic behavior for suitable potentials V . The case V = c1Ω for c > 0 and Ω a Borel set of finite measure is investigated in detail.