DIRICHLET HEAT KERNEL ESTIMATES FOR FRACTIONAL LAPLACIAN WITH GRADIENT PERTURBATION

被引：63

作者：

Chen, Zhen-Qing ^{[1
]}

Kim, Panki ^{[2
]}

Song, Renming ^{[3
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

ANNALS OF PROBABILITY | 2012年 / 40卷 / 06期

基金：

新加坡国家研究基金会;

关键词：

Symmetric alpha-stable process; gradient operator; heat kernel; transition density; Green function; exit time; Levy system; boundary Harnack inequality; Kato class; BOUNDARY HARNACK PRINCIPLE; HARMONIC-FUNCTIONS;

D O I：

10.1214/11-AOP682

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：2483 / 2538

页数：56

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[3]

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