Potential theory of Dirichlet forms with jump kernels blowing up at the boundary

2023.7.17 15:00 N620

In this talk, I will present some recent results on potential theory of Dirichlet forms on the half-space R^d_+defined by the jump kernel J(x,y) = |x − y| −d−α B(x,y), where α ∈ (0,2) and B(x,y) can blow up to infinity at the boundary. The main resultsinclude boundary Harnack principle and sharp two-sided Green function estimates.This talk is based on a joint paper with Panki Kim and Zoran Vondracek.