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

Format:

Book

Author/Creator:

Chen, Zhen-Qing.

Contributor:

Kumagai, Takashi.

Wang, Jian, 1979-

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.271

Language:

English

Subjects (All):

Kernel functions.

Physical Description:

1 online resource (102 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

"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"-- Provided by publisher.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references.

ISBN:

9781470466381

1470466384

OCLC:

1266906499