Time-dependent gradient perturbations of fractional Laplacian
Résumé
We construct a fundamental solution of the equation {\partial_t - \Delta^{\alpha/2} - b(\cdot, \cdot) \cdot\nabla_{x} = 0} for TeX{\alpha \in (1, 2)} and b satisfying a certain integral space-time condition. We also show it has α-stable upper and lower bounds.