scholarly journals Non-local Dirichlet forms and symmetric jump processes

2008 ◽  
Vol 361 (04) ◽  
pp. 1963-1999 ◽  
Author(s):  
Martin T. Barlow ◽  
Richard F. Bass ◽  
Zhen-Qing Chen ◽  
Moritz Kassmann
Keyword(s):  
Dirichlet Forms ◽  
Jump Processes ◽  
Non Local

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

scholarly journals Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory

2014 ◽  
Vol 266 (8) ◽  
pp. 4765-4808 ◽  
Author(s):  
Rupert L. Frank ◽  
Daniel Lenz ◽  
Daniel Wingert
Keyword(s):  
Spectral Theory ◽  
Dirichlet Forms ◽  
Intrinsic Metrics ◽  
Non Local

scholarly journals Stability of heat kernel estimates for symmetric non-local Dirichlet forms

2021 ◽  
Vol 271 (1330) ◽  
Author(s):  
Zhen-Qing Chen ◽  
Takashi Kumagai ◽  
Jian Wang
Keyword(s):  
Heat Kernel ◽  
Jump Processes ◽  
Metric Measure Spaces ◽  
Kernel Estimates ◽  
Open Problems ◽  
Content Type ◽  
Heat Kernel Estimates ◽  
Measure Spaces ◽  
Non Local ◽  
Volume Doubling

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 α \alpha -stable-like processes even with α ≥ 2 \alpha \ge 2 when the underlying spaces have walk dimensions larger than 2 2 , which has been one of the major open problems in this area.

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