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

University of Washington
Kyoto University
Fujian Normal University

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

18 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 - May 2019
Externally published	Yes

Keywords

Elliptic Harnack inequality
Hölder regularity
Non-local Dirichlet form
Stability

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10.1016/j.matpur.2017.10.011

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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.",

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AU - Chen, Zhen Qing

AU - Kumagai, Takashi

AU - Wang, Jian

PY - 2019/5

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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

Abstract

Keywords

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