Heat Kernels and Green Functions on Metric Measure Spaces
Grigoryan A, Hu J (2014)
Canadian Journal of Mathematics 66(3): 641-699.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Grigoryan, AlexanderUniBi;
Hu, Jiaxin
Einrichtung
Abstract / Bemerkung
We prove that, in a setting of local Dirichlet forms on metric measure spaces, a two-sided sub-Gaussian estimate of the heat kernel is equivalent to the conjunction of the volume doubling property, the elliptic Harnack inequality, and a certain estimate of the capacity between concentric balls. The main technical tool is the equivalence between the capacity estimate and the estimate of a mean exit time in a ball that uses two-sided estimates of a Green function in a ball.
Stichworte
Dirichlet form;
heat kernel;
Green function;
capacity
Erscheinungsjahr
2014
Zeitschriftentitel
Canadian Journal of Mathematics
Band
66
Ausgabe
3
Seite(n)
641-699
ISSN
0008-414X
Page URI
https://pub.uni-bielefeld.de/record/2684291
Zitieren
Grigoryan A, Hu J. Heat Kernels and Green Functions on Metric Measure Spaces. Canadian Journal of Mathematics. 2014;66(3):641-699.
Grigoryan, A., & Hu, J. (2014). Heat Kernels and Green Functions on Metric Measure Spaces. Canadian Journal of Mathematics, 66(3), 641-699. https://doi.org/10.4153/CJM-2012-061-5
Grigoryan, Alexander, and Hu, Jiaxin. 2014. “Heat Kernels and Green Functions on Metric Measure Spaces”. Canadian Journal of Mathematics 66 (3): 641-699.
Grigoryan, A., and Hu, J. (2014). Heat Kernels and Green Functions on Metric Measure Spaces. Canadian Journal of Mathematics 66, 641-699.
Grigoryan, A., & Hu, J., 2014. Heat Kernels and Green Functions on Metric Measure Spaces. Canadian Journal of Mathematics, 66(3), p 641-699.
A. Grigoryan and J. Hu, “Heat Kernels and Green Functions on Metric Measure Spaces”, Canadian Journal of Mathematics, vol. 66, 2014, pp. 641-699.
Grigoryan, A., Hu, J.: Heat Kernels and Green Functions on Metric Measure Spaces. Canadian Journal of Mathematics. 66, 641-699 (2014).
Grigoryan, Alexander, and Hu, Jiaxin. “Heat Kernels and Green Functions on Metric Measure Spaces”. Canadian Journal of Mathematics 66.3 (2014): 641-699.
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