Speaker
Panki Kim
(Seoul national University)
Description
In this talk, we discuss pure-jump Markov processes on smooth open sets whose jumping kernels vanishing at the boundary and part processes obtained by killing at the boundary or (and) by killing via the killing potential. The killing potential may be subcritical or critical.
This work can be viewed as developing a general theory for non-local singular operators whose kernel vanishing at the boundary. Due to the possible degeneracy at the boundary, such operators are, in a certain sense, not uniformly elliptic. These operators cover the restricted, censored and spectral Laplacians in smooth open sets and much more.
The main results are the boundary Harnack principle and its possible failure, and sharp two-sided Green function estimates.
Primary author
Panki Kim
(Seoul national University)
Co-authors
Prof.
Renming Song
(University of Illinois)
Prof.
Soobin Cho
(University of Illinois)
Prof.
Zoran Vondracek
(University of Zagreb)
