Title: Heat kernel estimates for Markov processes with jump kernels blowing-up at the boundary
Speaker: 宋仁明（伊利诺伊大学厄巴纳-香槟分校）
Time: 1.9 (Friday), 10:50-11:30
Venue: 活动中心331
Abstract:
In this talk, I will present some recent results about purely discontinuous symmetric Markov processes on closed subsets of Rd , d ≥ 1, with jump kernels of the form J(x, y) = |x − y|-d-α B(x, y), α ∈ (0, 2), where the function B(x, y) may blow up at the boundary of the state space.
Examples of Markov processes that fall into our general framework include traces of isotropic α-stable processes in C1,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. A fundamental difficulty in accomplishing this task is that, in contrast to the existing literature on heat kernels for jump processes, the tails of the associated jump measures in our setting are not uniformly bounded.
Thus, standard techniques in the existing literature used to study heat kernels are not applicable.To overcome this obstacle, we employ recently developed weighted functional inequalities specifically designed for jump kernels blowing up at the boundary. This talk is based on a joint paper with Soobin Cho, Panki Kim and Zoran Vondracek.
