Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients

被引：0
|
作者：
Renming Song
Longjie Xie
Yingchao Xie
机构：
[1] University of Illinois at Urbana-Champaign,Department of Mathematics
[2] Jiangsu Normal University,School of Mathematics and Statistics
来源：
Science China Mathematics | 2020年 / 63卷
关键词：
spectral fractional Laplacian; Dirichlet heat kernel; Kato class; gradient estimate; 60J35; 60J50;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Using Duhamel’s formula, we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C1,1 domains. In addition, we obtain a gradient estimate as well as the Hölder continuity of the heat kernel’s gradient.
引用
收藏
页码：2343 / 2362
页数：19
相关论文
共 50 条
  • [1] Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients
    Renming Song
    Longjie Xie
    Yingchao Xie
    [J]. Science China Mathematics, 2020, 63 (11) : 2343 - 2362
  • [2] Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients
    Song, Renming
    Xie, Longjie
    Xie, Yingchao
    [J]. SCIENCE CHINA-MATHEMATICS, 2020, 63 (11) : 2343 - 2362
  • [3] Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators
    Krzysztof Bogdan
    Tomasz Jakubowski
    [J]. Communications in Mathematical Physics, 2007, 271 : 179 - 198
  • [4] Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
    Bogdan, Krzysztof
    Jakubowski, Tomasz
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 271 (01) : 179 - 198
  • [5] Heat kernel estimates for the Dirichlet fractional Laplacian
    Chen, Zhen-Qing
    Kim, Panki
    Song, Renming
    [J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2010, 12 (05) : 1307 - 1329
  • [6] HEAT KERNEL ESTIMATES FOR THE FRACTIONAL LAPLACIAN WITH DIRICHLET CONDITIONS
    Bogdan, Krzysztof
    Grzywny, Tomasz
    Ryznar, Michal
    [J]. ANNALS OF PROBABILITY, 2010, 38 (05): : 1901 - 1923
  • [7] HEAT KERNEL ESTIMATES FOR DIRICHLET FRACTIONAL LAPLACIAN WITH GRADIENT PERTURBATION
    Chen, Peng
    Song, Renming
    Xie, Longjie
    Xie, Yingchao
    [J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2019, 56 (01) : 91 - 111
  • [8] DIRICHLET HEAT KERNEL ESTIMATES FOR FRACTIONAL LAPLACIAN WITH GRADIENT PERTURBATION
    Chen, Zhen-Qing
    Kim, Panki
    Song, Renming
    [J]. ANNALS OF PROBABILITY, 2012, 40 (06): : 2483 - 2538
  • [9] Sharp estimates of the spherical heat kernel
    Nowak, Adam
    Sjogren, Peter
    Szarek, Tomasz Z.
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 129 : 23 - 33
  • [10] Sharp estimates of the Jacobi heat kernel
    Nowak, Adam
    Sjogren, Peter
    [J]. STUDIA MATHEMATICA, 2013, 218 (03) : 219 - 244
12345