Geodesic
Heat Kernels and Green Functions on Metric Measure Spaces
Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 641-699

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DOI

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.
DOI : 10.4153/CJM-2012-061-5
Mots-clés : 35K08, 28A80, 31B05, 35J08, 46E35, 47D07, Dirichlet form, heat kernel, Green function, capacity 
Grigor'yan, Alexander; Hu, Jiaxin. Heat Kernels and Green Functions on Metric Measure Spaces. Canadian journal of mathematics, Tome 66 (2014) no. 3, pp. 641-699. doi: 10.4153/CJM-2012-061-5
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