On fractional Leibniz rule for dirichlet laplacian in exterior domain

Vladimir Georgiev; Koichi Taniguchi

doi:10.3934/dcds.2019046

On fractional Leibniz rule for dirichlet laplacian in exterior domain

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1101-1115
Number of pages	15
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	39
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2019046
Publication status	Published - 2019 Feb
Externally published	Yes

Keywords

Dirichlet problem
Exterior domains
Fractional Leibniz rule
Gradient estimates
Heat equations

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2019046

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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",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

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AU - Georgiev, Vladimir

AU - Taniguchi, Koichi

N1 - 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’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: © 2019 American Institute of Mathematical Sciences. All rights reserved.

PY - 2019/2

Y1 - 2019/2

N2 - 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.

AB - 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.

KW - Dirichlet problem

KW - Exterior domains

KW - Fractional Leibniz rule

KW - Gradient estimates

KW - Heat equations

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JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 2

ER -

On fractional Leibniz rule for dirichlet laplacian in exterior domain

Abstract

Keywords

ASJC Scopus subject areas

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