HEAT KERNEL ESTIMATES FOR DIRICHLET FRACTIONAL LAPLACIAN WITH GRADIENT PERTURBATION

被引：4

作者：

Chen, Peng ^{[1
]}

Song, Renming ^{[2
]}

Xie, Longjie ^{[3
]}

Xie, Yingchao ^{[3
]}

机构：

[1] Univ Macau, Dept Math, Macau, Peoples R China

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221000, Jiangsu, Peoples R China

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2019年 / 56卷 / 01期

关键词：

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

D O I：

10.4134/JKMS.j180065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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,C-theta for some theta is an element of (alpha/2,1].

引用

页码：91 / 111

页数：21

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