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http://dx.doi.org/10.4134/JKMS.j180065

HEAT KERNEL ESTIMATES FOR DIRICHLET FRACTIONAL LAPLACIAN WITH GRADIENT PERTURBATION

Chen, Peng (Department of Mathematics University of Macau)
Song, Renming (Department of Mathematics University of Illinois)
Xie, Longjie (School of Mathematics and Statistics Jiangsu Normal University)
Xie, Yingchao (School of Mathematics and Statistics Jiangsu Normal University)

Publication Information

Journal of the Korean Mathematical Society / v.56, no.1, 2019 , pp. 91-111 More about this Journal

Abstract

We give a direct proof of the sharp two-sided estimates, recently established in [4, 9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in $C^{1,1}$ open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be $C^{1,{\theta}}$ for some $${\theta}{\in}({\alpha}/2,1$ $]$ $$$ .

Keywords

isotropic stable process; fractional Laplacian; Dirichlet heat kernel; Kato class; gradient estimate;

Citations & Related Records

Reference

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