Heat kernel estimates for $\Delta +{\Delta }^{\alpha /2}$ under gradient perturbation

Zhen-Qing Chen, Eryan Hu

For $d\ge 2$, $\alpha \in (0,2)$ and $M>0$, we consider the gradient perturbation of a family of nonlocal operators $\{\Delta +a^{\alpha }{\Delta }^{\alpha /2},a\in (0,M]\}$. We establish the existence and uniq…