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

Zhen-Qing Chen; Panki Kim; Renming Song

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arXiv · 1112.3401

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

Zhen-Qing Chen·Panki Kim·Renming Song

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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 on closed $d$-sets in $\bR^d$, 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.

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BibTeX RIS

Zhen-Qing Chen, Panki Kim, Renming Song. 2011-12-15. Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-Kac perturbation. https://arxiv.org/abs/1112.3401

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