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

Alexander Grigor'yan, Shunxiang Ouyang, Michael Röckner

We prove upper and lower bounds of the heat kernel for the operator $\Delta -\nabla (\frac{1}{|x{|}^{\alpha }})\cdot \nabla$ in $\mathbb{R}^{n}\setminus\{0} $ where $\alpha >0$. We obtain these bounds…