Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition
Liu G (2024)
Journal of Mathematical Analysis and Applications 539(1): 128477.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Abstract / Bemerkung
In this paper, we focus on the heat kernel estimates for diffusions and jump processes on metric measure spaces satisfying a weak chain condition, where the length of a nearly shortest epsilon-chain between two points x, y is comparable with a function of d(x, y) and epsilon. For a diffusion, the best estimate is already given by Grigor'yan and Telcs, and we make it explicit in our particular case. For jump processes, especially those where the scale of the process is different with that of the jump kernel, we improve the results by Bae, Kang, Kim and Lee. Uniformity of the coefficients (or parameters) in the known estimates and metric transforms play the key role in our proof. We also show by examples how the weak chain condition is valid in practice. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http://creativecommons .org /licenses /by -nc /4 .0/).
Stichworte
Heat kernel estimates;
Jump processes;
Diffusions;
Metric measure;
spaces;
Weak chain conditions
Erscheinungsjahr
2024
Zeitschriftentitel
Journal of Mathematical Analysis and Applications
Band
539
Ausgabe
1
Art.-Nr.
128477
ISSN
0022-247X
eISSN
1096-0813
Page URI
https://pub.uni-bielefeld.de/record/2990747
Zitieren
Liu G. Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition. Journal of Mathematical Analysis and Applications . 2024;539(1): 128477.
Liu, G. (2024). Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition. Journal of Mathematical Analysis and Applications , 539(1), 128477. https://doi.org/10.1016/j.jmaa.2024.128477
Liu, Guanhua. 2024. “Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition”. Journal of Mathematical Analysis and Applications 539 (1): 128477.
Liu, G. (2024). Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition. Journal of Mathematical Analysis and Applications 539:128477.
Liu, G., 2024. Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition. Journal of Mathematical Analysis and Applications , 539(1): 128477.
G. Liu, “Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition”, Journal of Mathematical Analysis and Applications , vol. 539, 2024, : 128477.
Liu, G.: Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition. Journal of Mathematical Analysis and Applications . 539, : 128477 (2024).
Liu, Guanhua. “Heat kernel estimates on local and non-local Dirichlet spaces satisfying a weak chain condition”. Journal of Mathematical Analysis and Applications 539.1 (2024): 128477.
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