@article{05c2b0ab4cc64bc987321467e818acc5,
title = "Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients",
abstract = "Using Duhamel{\textquoteright}s formula, we prove sharp two-sided estimates for the spectral fractional Laplacian{\textquoteright}s heat kernel with time-dependent gradient perturbation in bounded C1,1 domains. In addition, we obtain a gradient estimate as well as the H{\"o}lder continuity of the heat kernel{\textquoteright}s gradient.",
keywords = "60J35, 60J50, Dirichlet heat kernel, Kato class, gradient estimate, spectral fractional Laplacian",
author = "Renming Song and Longjie Xie and Yingchao Xie",
note = "Funding Information: The first author was supported by the Simons Foundation (Grant No. #429343). The second author was supported by the Alexander-von-Humboldt Foundation, National Natural Science Foundation of China (Grant No. 11701233) and National Science Foundation of Jiangsu (Grant No. BK20170226). The third author was supported by National Natural Science Foundation of China (Grant No. 11771187). The Priority Academic Program Development of Jiangsu Higher Education Institutions is also gratefully acknowledged. The authors thank the referees for carefully reading the manuscript and providing many helpful suggestions. Publisher Copyright: {\textcopyright} 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2020",
month = nov,
day = "1",
doi = "10.1007/s11425-018-9472-x",
language = "English (US)",
volume = "63",
pages = "2343--2362",
journal = "Science China Mathematics",
issn = "1674-7283",
publisher = "Science in China Press",
number = "11",
}