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^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	1-42
Number of pages	42
Journal	Journal des Mathematiques Pures et Appliquees
Volume	125
DOIs	https://doi.org/10.1016/j.matpur.2017.10.011
Publication status	Published - 2019 May
Externally published	Yes

Keywords

Elliptic Harnack inequality
Hölder regularity
Non-local Dirichlet form
Stability

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1016/j.matpur.2017.10.011

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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 = "Funding Information: The research of Takashi Kumagai is supported by the Grant-in-Aid for Scientific Research (A) 25247007 and 17H01093 , Japan. The research of Jian Wang is supported by National Natural Science Foundation of China (Nos. 11522106 and 11831014 ), the JSPS postdoctoral fellowship ( 26⋅04021 ), Fok Ying Tung Education Foundation (No. 151002 ), National Science Foundation of Fujian Province (No. 2015J01003 ), the Program for Probability and Statistics: Theory and Application (No. IRTL1704 ), and Fujian Provincial Key Laboratory of Mathematical Analysis and its Applications (FJKLMAA). We thank the referee for helpful comments on the paper. Publisher Copyright: {\textcopyright} 2017 Elsevier Masson SAS",

year = "2019",

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

language = "English",

volume = "125",

pages = "1--42",

journal = "Journal des Mathematiques Pures et Appliquees",

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

AU - Chen, Zhen Qing

AU - Kumagai, Takashi

AU - Wang, Jian

N1 - Funding Information: The research of Takashi Kumagai is supported by the Grant-in-Aid for Scientific Research (A) 25247007 and 17H01093 , Japan. The research of Jian Wang is supported by National Natural Science Foundation of China (Nos. 11522106 and 11831014 ), the JSPS postdoctoral fellowship ( 26⋅04021 ), Fok Ying Tung Education Foundation (No. 151002 ), National Science Foundation of Fujian Province (No. 2015J01003 ), the Program for Probability and Statistics: Theory and Application (No. IRTL1704 ), and Fujian Provincial Key Laboratory of Mathematical Analysis and its Applications (FJKLMAA). We thank the referee for helpful comments on the paper. Publisher Copyright: © 2017 Elsevier Masson SAS

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

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ER -

Elliptic Harnack inequalities for symmetric non-local Dirichlet forms

Abstract

Keywords

ASJC Scopus subject areas

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