Markov processes with jump kernel decaying at the boundary

报告专家:Panki Kim(Seoul national university)



报告摘要: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.

专家简介:Panki Kim为韩国首尔国立大学教授,2004年从美国华盛顿大学获得博士学位。2004.8-2006.8,在美国伊利罗伊香槟分校担任助理教授;2006.9-2008.9,韩国首尔国立大学助理教授;2008.10-2013.8, 首尔国立大学副教授;2013年9月至今,首尔国立大学教授。2013.7-2019.6, 担任杂志Journal of Korean Mathematical Society的编委。