CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 35J08 ( Green's functions )

  Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2013 (vol 66 pp. 641)

Grigor'yan, Alexander; Hu, Jiaxin
Heat Kernels and Green Functions on Metric Measure Spaces
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 propety, 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.

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

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/