Dirichlet Heat Kernel Estimates for Stable Processes with Singular Drift In Unbounded C1,1 Open Sets

摘要

Suppose d ≥ 2 and α ∈ (1, 2). Let D be a (not necessarily bounded) C~(1,1) open set in Rd and μ = (μ~1,...,μ~d) where each μj is a signed measure on Rd belonging to a certain Kato class of the rotationally symmetric α-stable process X. Let X~μ be an α-stable process with drift μ in Rd and let X~μ,D be the subprocess of X~μ in D. In this paper, we derive sharp two-sided estimates for the transition density of X~(μ,D).