Resumen de Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation

Zhen-Qing Chen, Panki Kim, Renming Song

• Suppose that d≥2 and α∈(1,2). Let D be a bounded C1,1 open set in Rd and b an Rd-valued function on Rd whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for Lb=Δα/2+b⋅∇ in D with zero exterior condition. We also obtain the boundary Harnack principle for Lb in D with explicit decay rate.