Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities
Grigoryan, Alexander
Grigoryan
Alexander
Ouyang, Shunxiang
Ouyang
Shunxiang
Röckner, Michael
Röckner
Michael
In the present paper we prove upper and lower bounds of the heat kernel for the operator Delta - del(vertical bar x vertical bar(-alpha) ) . del in R-n \ {0} where alpha > 0. We obtain these bounds from an isoperimetric inequality for a measure e(-vertical bar x vertical bar-alpha) dx on R-n \ {0}. The latter amounts to a certain functional isoperimetric inequality for the radial part of this measure.
736
736
1-31
1-31
Walter De Gruyter Gmbh
2018