Renming Song (UIUC)
罢颈迟濒别:听Heat kernel estimates for Markov processes with jump kernels blowing-up at the boundary
Abstract: In this talk, I will present some recent results about purely discontinuous symmetric Markov processes on closed subsets of ${\mathbb R}^d$, $d\ge 1$, with jump kernels of the form $J(x,y)=|x-y|^{-d-\alpha}{\mathcal B}(x,y)$, $\alpha\in (0,2)$, where the function ${\mathcal B}(x,y)$ may blow up at the boundary of the state space.
We study both conservative Markov processes of this type and critically killed Markov processes of this type. Examples of Markov processes that fall into our general framework include traces of isotropic $\alpha$-stable processes in $C^{1,\rm Dini}$ sets, processes in Lipschitz sets arising in connection with the nonlocal Neumann problem, and a large class of resurrected self-similar processes in the closed upper half-space. Our main results are sharp two-sided heat kernel estimates for these Markov processes. This talk is based on joint works with Soobin Cho, Panki Kim and Zoran Vondracek.
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