Zhen-Qing Chen, Panki Kim, Renming Song
Published 2011-12-15Version 1
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.
Dirichlet Heat Kernel Estimates for Rotationally Symmetric Lévy processes
Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in $C^{1,η}$ open sets
Heat Kernel Estimate for $Δ+Δ^{α/2}$ in $C^{1,1}$ open sets
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