@article{ce1afa4c89c44296aef32b665a0405c9,
title = "On fractional Leibniz rule for dirichlet laplacian in exterior domain",
abstract = "The goal of the work is to verify the fractional Leibniz rule for Dirichlet Laplacian in the exterior domain of a compact set. The key point is the proof of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet problem.",
keywords = "Dirichlet problem, Exterior domains, Fractional Leibniz rule, Gradient estimates, Heat equations",
author = "Vladimir Georgiev and Koichi Taniguchi",
note = "Funding Information: The first author was supported in part by Project 2017 “Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari” of INDAM, GNAMPA - Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilita e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, by Top Global University Project, Waseda University and the Project PRA 2018 49 of University of Pisa. Publisher Copyright: {\textcopyright} 2019 American Institute of Mathematical Sciences. All rights reserved.",
year = "2019",
month = feb,
doi = "10.3934/dcds.2019046",
language = "English",
volume = "39",
pages = "1101--1115",
journal = "Discrete and Continuous Dynamical Systems- Series A",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "2",
}