[GS_M_APP] Heat kernel estimates for local and nonlocal Schrödinger operators with supercritical killing
ABSTRACT
In this talk, we discuss heat kernel estimates for local and nonlocal Schrödinger operators with supercritical killing potentials. A prototypical example is $-(-\Delta)^s - \kappa |x|^{-2(s+\gamma)}$, $\kappa,\gamma>0$. We present both probabilistic and analytic approaches to the study of these operators. We highlight the fundamental differences in the results for the local and nonlocal settings and examine how they differ from those in the critical case ($\gamma=0$). The talk is based on joint work with Renming Song (UIUC) and Panki Kim (SNU).
