Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms

• Autore: Chen Zhen-Qing
• Pubblicazione: Providence : , : American Mathematical Society, , 2021; ©2021
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (102 pages)
• Disciplina: 519.2/33
• Soggetto topico: Kernel functions; Probability theory and stochastic processes -- Markov processes -- Transition functions, generators and resolvents; Partial differential equations -- Parabolic equations and systems -- Heat kernel; Probability theory and stochastic processes -- Markov processes -- Jump processes; Potential theory -- Other generalizations -- Dirichlet spaces; Probability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on general state spaces; Probability theory and stochastic processes -- Markov processes -- Probabilistic potential theory
• Classificazione: 60J3535K0860J7531C2560J2560J45
• Altri autori: KumagaiTakashi WangJian <1979->
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Cover -- Title page -- Chapter 1. Introduction and Main Results -- 1. Setting -- 2. Heat kernel -- Chapter 2. Preliminaries -- Chapter 3. Implications of heat kernel estimates -- 1. \UHK( )+(\sE,\sF) ⟹\J_{ ,≤}, and \HK( )⟹\Jᵩ -- 2. \UHK( ) (\sE,\sF) ⟹\SCSJ( ) -- Chapter 4. Implications of \CSJ( ) and \J_{ ,≥} -- 1. \J_{ ,≥}⟹\FK( ) -- 2. Caccioppoli and ¹-mean value inequalities -- 3. \FK( )+\J_{ ,≤}+\CSJ( )⟹\Eᵩ -- 4. \FK( )+\Eᵩ+\J_{ ,≤}⟹\UHKD( ) -- Chapter 5. Consequences of condition \Jᵩ and mean exit time condition \Eᵩ -- 1. \UHKD( )+\J_{ ,≤}+\Eᵩ⟹\UHK( ), \Jᵩ+\Eᵩ⟹\UHK( ) -- 2. \Jᵩ+\Eᵩ⟹\LHK( ) -- Chapter 6. Applications and Examples -- 1. Applications -- 2. Counterexample -- Chapter 7. Appendix -- 1. Lévy system formula -- 2. Meyer's decomposition -- 3. Some results related to \FK( ). -- 4. Some results related to (Dirichlet) heat kernel -- 5. \SCSJ( )+\J_{ ,≤}⟹(\sE,\sF) is conservative -- Acknowledgment -- Bibliography -- Back Cover.
• Sommario/riassunto: "In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particular, we establish stability of heat kernel estimates for -stable-like processes even with 2 when the underlying spaces have walk dimensions larger than 2, which has been one of the major open problems in this area"--
• Titolo autorizzato: Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms
• ISBN: 9781470466381; 1470466384
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910974261603321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society