Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation

Chen, Zhen-Qing; Kim, Panki; Song, Renming

doi:10.1090/S0002-9947-2014-06190-4

Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation
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Trans. Amer. Math. Soc. 367 (2015), 5237-5270 Request permission

Abstract:

In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under non-local Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed $d$-sets in $\mathbb {R}^d$, killed symmetric stable processes, censored stable processes in $C^{1, 1}$ open sets, as well as stable processes with drifts in bounded $C^{1, 1}$ open sets. These two-sided estimates are explicit involving distance functions to the boundary.

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