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.
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。
