@article{f61519825a544a8ea8cb427613cda947,
title = "Dirichlet heat kernel estimates for fractional laplacian with gradient perturbation",
abstract = "Suppose that d ≥ 2 and α ∈ (1, 2). Let D be a bounded C1,1 open set in Rd and b an Rd -valued function on Rd whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for Lb = δα/2 + b. ∇ in D with zero exterior condition. We also obtain the boundary Harnack principle for Lb in D with explicit decay rate.",
keywords = "Boundary harnack inequality, Exit time, Gradient operator, Green function, Heat kernel, Kato class, L{\'e}vy system, Symmetric α-stable process, Transition density",
author = "Chen, {Zhen Qing} and Panki Kim and Renming Song",
year = "2012",
doi = "10.1214/11-AOP682",
language = "English",
volume = "40",
pages = "2483--2538",
journal = "Annals of Probability",
issn = "0091-1798",
publisher = "Institute of Mathematical Statistics",
number = "6",
}