Fractional Laplacian with supercritical killings

2024/03/05 by Cho, Soobin, Song, Renming
#60G51 #60J25 #60J35 #60J76 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2403.03298

Abstract

In this paper, we study Feynman-Kac semigroups of symmetric α-stable processes with supercritical killing potentials belonging to a large class of functions containing functions of the form b|x|^-β, where b>0 and β>α. We obtain two-sided estimates on the densities p(t, x, y) of these semigroups for all t>0, along with estimates for the corresponding Green functions.

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