Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

被引：16

作者：

Chen, Zhen-Qing ^{[1
]}

Kumagai, Takashi ^{[2
]}

Wang, Jian ^{[3
,4
]}

机构：

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

[2] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan

[3] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350007, Fujian, Peoples R China

[4] Fujian Normal Univ, Fujian Key Lab Math Anal & Applicat FJKLMAA, Fuzhou 350007, Fujian, Peoples R China

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 125卷

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Non-local Dirichlet form; Elliptic Harnack inequality; Holder regularity; Stability; HEAT KERNELS; JUMP-PROCESSES; UPPER-BOUNDS; REGULARITY; EQUATIONS; THEOREM; MINIMA;

D O I：

10.1016/j.matpur.2017.10.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study relations and characterizations of various elliptic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces. We allow the scaling function be state-dependent and the state space possibly disconnected. Stability of elliptic Harnack inequalities is established under certain regularity conditions and implication for a priori Holder regularity of harmonic functions is explored. New equivalent statements for parabolic Harnack inequalities of non-local Dirichlet forms are obtained in terms of elliptic Harnack inequalities. (C) 2017 Elsevier Masson SAS. All rights reserved.

引用

页码：1 / 42

页数：42

共 40 条

[1]

[Anonymous], 2003, DIRECT METHODS CALCU, DOI DOI 10.1142/5002

[2]

Barlow M. T., 2016, ANN MATH

[3] Heat kernel upper bounds for jump processes and the first exit time [J].