Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities

2012/11/27 by Grigor'yan, Alexander, Ouyang, Shunxiang, Röckner, Michael
#26D10 #28A75 #58J35 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1211.6169

Abstract

We prove upper and lower bounds of the heat kernel for the operator Δ-∇ ((1)/(|x|^α))⋅ ∇ in ℝⁿ∖\0 where α>0. We obtain these bounds from an isoperimetric inequality for a measure e^-(1)/(|x|α)dx on ℝⁿ∖ \0\. The latter amounts to a certain functional isoperimetric inequality for the radial part of this measure.

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