Mean value inequalities for jump processes

Zhen Qing Chen, Takashi Kumagai*, Jian Wang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Parabolic Harnack inequalities are one of the most important inequalities in analysis and PDEs, partly because they imply Hölder regularity of the solutions of heat equations. Mean value inequalities play an important role in deriving parabolic Harnack inequalities. In this paper, we first survey the recent results obtained in Chen et al. (Stability of heat kernel estimates for symmetric non-local Dirichlet forms, 2016, [15]; Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms, 2016, [16]) on the study of stability of heat kernel estimates and parabolic Harnack inequalities for symmetric jump processes on general metric measure spaces. We then establish the Lp -mean value inequalities for all p∈ (0, 2] for these processes.

Original languageEnglish
Title of host publicationStochastic Partial Differential Equations and Related Fields - In Honor of Michael Röckner SPDERF, 2016
EditorsGerald Trutnau, Andreas Eberle, Walter Hoh, Moritz Kassmann, Martin Grothaus, Wilhelm Stannat
PublisherSpringer New York LLC
Pages421-437
Number of pages17
ISBN (Print)9783319749280
DOIs
Publication statusPublished - 2018
Externally publishedYes
EventInternational conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016 - Bielefeld, Germany
Duration: 2016 Oct 102016 Oct 14

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume229
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherInternational conference on Stochastic Partial Differential Equations and Related Fields, SPDERF 2016
Country/TerritoryGermany
CityBielefeld
Period16/10/1016/10/14

Keywords

  • Harnack inequality
  • Heat kernel estimate
  • Mean value inequality
  • Stability
  • Symmetric jump process

ASJC Scopus subject areas

  • General Mathematics

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