DIRICHLET HEAT KERNEL ESTIMATES FOR FRACTIONAL LAPLACIAN WITH GRADIENT PERTURBATION

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Kim, Panki; Song, Renming
• 署名单位: University of Washington; University of Washington Seattle; Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP682
• 发表日期: 2012
• 页码: 2483-2538
• 关键词: boundary harnack principle; harmonic-functions

摘要

Suppose that d >= 2 and alpha is an element of (1, 2). Let D be a bounded C-1,C-1 open set in R-d and b an R-d-valued function on R-d whose components are in a certain Kato class of the rotationally symmetric a-stable process. In this paper, we derive sharp two-sided heat kernel estimates for L-b = Delta(alpha/2) + b . del in D with zero exterior condition. We also obtain the boundary Harnack principle for L-b in D with explicit decay rate.