Heat Kernels and Green Functions on Metric Measure Spaces

Grigor'yan, Alexander ; Hu, Jiaxin

Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 641-699

Résumé

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.

Détail

DOI : 10.4153/CJM-2012-061-5

Mots-clés : 35K08, 28A80, 31B05, 35J08, 46E35, 47D07, Dirichlet form, heat kernel, Green function, capacity

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