Generalized capacity, harnack inequality and heat kernels of dirichlet forms on metric measure spaces

Grigoryan A, Hu J, Lau K-S (2015)
Journal of the Mathematical Society of Japan 67(4): 1485-1549.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Grigoryan, AlexanderUniBi; Hu, Jiaxin; Lau, Ka-Sing
Abstract / Bemerkung
We give necessary and sufficient conditions for sub-Gaussian estimates of the heat kernel of a strongly local regular Dirichlet form on a metric measure space. The conditions for two-sided estimates are given in terms of the generalized capacity inequality and the Poincare inequality. The main difficulty lies in obtaining the elliptic Harnack inequality under these assumptions. The conditions for upper bound alone are given in terms of the generalized capacity inequality and the Faber-Krahn inequality.
Stichworte
generalized capacity
Erscheinungsjahr
2015
Zeitschriftentitel
Journal of the Mathematical Society of Japan
Band
67
Ausgabe
4
Seite(n)
1485-1549
ISSN
0025-5645
Page URI
https://pub.uni-bielefeld.de/record/2901225

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Grigoryan A, Hu J, Lau K-S. Generalized capacity, harnack inequality and heat kernels of dirichlet forms on metric measure spaces. Journal of the Mathematical Society of Japan. 2015;67(4):1485-1549.
Grigoryan, A., Hu, J., & Lau, K. - S. (2015). Generalized capacity, harnack inequality and heat kernels of dirichlet forms on metric measure spaces. Journal of the Mathematical Society of Japan, 67(4), 1485-1549. doi:10.2969/jmsj/06741485
Grigoryan, A., Hu, J., and Lau, K. - S. (2015). Generalized capacity, harnack inequality and heat kernels of dirichlet forms on metric measure spaces. Journal of the Mathematical Society of Japan 67, 1485-1549.
Grigoryan, A., Hu, J., & Lau, K.-S., 2015. Generalized capacity, harnack inequality and heat kernels of dirichlet forms on metric measure spaces. Journal of the Mathematical Society of Japan, 67(4), p 1485-1549.
A. Grigoryan, J. Hu, and K.-S. Lau, “Generalized capacity, harnack inequality and heat kernels of dirichlet forms on metric measure spaces”, Journal of the Mathematical Society of Japan, vol. 67, 2015, pp. 1485-1549.
Grigoryan, A., Hu, J., Lau, K.-S.: Generalized capacity, harnack inequality and heat kernels of dirichlet forms on metric measure spaces. Journal of the Mathematical Society of Japan. 67, 1485-1549 (2015).
Grigoryan, Alexander, Hu, Jiaxin, and Lau, Ka-Sing. “Generalized capacity, harnack inequality and heat kernels of dirichlet forms on metric measure spaces”. Journal of the Mathematical Society of Japan 67.4 (2015): 1485-1549.

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