Harnack inequalities for non-local operators of variable order

被引：90

作者：

Bass, RF ^{[1
]}

Kassmann, M

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

[2] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 357卷 / 02期

关键词：

Harnack inequality; non-local operator; stable processes; Levy processes; jump processes; integral operators;

D O I：

10.1090/S0002-9947-04-03549-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider harmonic functions with respect to the operator Lu(x) = integral [u(x + h) - u(x)-1((\h\ less than or equal to 1))h . delu(x)]n(x, h)dh. Under suitable conditions on n(x, h) we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator L is allowed to be anisotropic and of variable order.

引用

页码：837 / 850

页数：14

共 20 条

[1]

Barlow MT, 2000, COMMUN PUR APPL MATH, V53, P1007, DOI 10.1002/1097-0312(200008)53:8<1007::AID-CPA3>3.3.CO

[2]

2-L

[3] UNIQUENESS IN LAW FOR PURE JUMP MARKOV-PROCESSES [J].