Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients  

作　　者：Renming Song Longjie Xie Yingchao Xie 

机构地区：[1]Department of Mathematics,University of Illinois at Urbana-Champaign,Urbana,IL 61801,USA [2]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221000,China

出　　处：《Science China Mathematics》2020年第11期2343-2362,共20页中国科学：数学（英文版）

基　　金：supported by the Simons Foundation(Grant No.#429343);supported by the Alexander-von-Humboldt Foundation;National Natural Science Foundation of China(Grant No.11701233);National Science Foundation of Jiangsu(Grant No.BK20170226);supported by National Natural Science Foundation of China(Grant No.11771187);The Priority Academic Program Development of Jiangsu Higher Education Institutions。

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 C^1,1 domains.In addition,we obtain a gradient estimate as well as the Holder continuity of the heat kernel’s gradient.

关 键 词：spectral fractional Laplacian Dirichlet heat kernel Kato class gradient estimate 

分 类 号：O552[理学—热学与物质分子运动论] O177[理学—物理]