Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation

• Autores: Zhen-Qing Chen, Panki Kim, Renming Song
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 40, Nº. 6, 2012, págs. 2483-2538
• Idioma: inglés
• DOI: 10.1214/11-AOP682
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• Resumen

  • 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.