Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation

الأصل · EN

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.