Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

Zhen Qing Chen; Takashi Kumagai; Jian Wang

doi:10.1016/j.matpur.2017.10.011

Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

Zhen Qing Chen
, Takashi Kumagai
, Jian Wang^*

^*此作品的通讯作者

University of Washington
Kyoto University
Fujian Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

18 引用（Scopus）

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 Hölder 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.

源语言	英语
页（从-至）	1-42
页数	42
期刊	Journal des Mathematiques Pures et Appliquees
卷	125
DOI	https://doi.org/10.1016/j.matpur.2017.10.011
出版状态	已出版 - 5月 2019
已对外发布	是

访问文件

10.1016/j.matpur.2017.10.011

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{5fd16158f1b04b3faa49fbda30514f14,

title = "Elliptic Harnack inequalities for symmetric non-local Dirichlet forms",

abstract = "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 H{\"o}lder 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.",

keywords = "Elliptic Harnack inequality, H{\"o}lder regularity, Non-local Dirichlet form, Stability",

author = "Chen, \{Zhen Qing\} and Takashi Kumagai and Jian Wang",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Masson SAS",

year = "2019",

month = may,

doi = "10.1016/j.matpur.2017.10.011",

language = "English",

volume = "125",

pages = "1--42",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson s.r.l.",

}

TY - JOUR

T1 - Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

AU - Chen, Zhen Qing

AU - Kumagai, Takashi

AU - Wang, Jian

PY - 2019/5

Y1 - 2019/5

N2 - 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 Hölder 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.

AB - 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 Hölder 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.

KW - Elliptic Harnack inequality

KW - Hölder regularity

KW - Non-local Dirichlet form

KW - Stability

UR - https://www.scopus.com/pages/publications/85064085209

U2 - 10.1016/j.matpur.2017.10.011

DO - 10.1016/j.matpur.2017.10.011

M3 - Article

AN - SCOPUS:85064085209

SN - 0021-7824

VL - 125

SP - 1

EP - 42

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

摘要

访问文件

其它文件与链接

学术指纹

引用此