Isoperimetric inequalities for the cauchy-dirichlet heat operator

Tynysbek Sh Kal’menov; Aidyn Kassymov; Durvudkhan Suragan

doi:10.2298/FIL1803885K

Isoperimetric inequalities for the cauchy-dirichlet heat operator

Tynysbek Sh Kal’menov, Aidyn Kassymov, Durvudkhan Suragan

Nazarbayev University

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

1 Citation (Scopus)

Abstract

In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in a circular cylinder among all Euclidean cylindric domains of a given measure. It is an analogue of the Rayleigh-Faber-Krahn inequality for the heat operator. We also prove a Hong-Krahn-Szegö and a Payne-Pólya-Weinberger type inequalities for the Cauchy-Dirichlet heat operator.

Original language	English
Pages (from-to)	885-892
Number of pages	8
Journal	Filomat
Volume	32
Issue number	3
DOIs	https://doi.org/10.2298/FIL1803885K
Publication status	Published - Jan 1 2018

Keywords

Cauchy-Dirichlet heat operator
Hong-Krahn-Szegö inequality
Payne-Pólya-weinberger inequality
Rayleigh-Faber-Krahn inequality
S-number

ASJC Scopus subject areas

General Mathematics

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10.2298/FIL1803885K

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title = "Isoperimetric inequalities for the cauchy-dirichlet heat operator",

abstract = "In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in a circular cylinder among all Euclidean cylindric domains of a given measure. It is an analogue of the Rayleigh-Faber-Krahn inequality for the heat operator. We also prove a Hong-Krahn-Szeg{\"o} and a Payne-P{\'o}lya-Weinberger type inequalities for the Cauchy-Dirichlet heat operator.",

keywords = "Cauchy-Dirichlet heat operator, Hong-Krahn-Szeg{\"o} inequality, Payne-P{\'o}lya-weinberger inequality, Rayleigh-Faber-Krahn inequality, S-number",

author = "Kal{\textquoteright}menov, {Tynysbek Sh} and Aidyn Kassymov and Durvudkhan Suragan",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary 35P05; Secondary 58J50 Keywords. Cauchy-Dirichlet heat operator, s-number, Rayleigh-Faber-Krahn inequality, Hong-Krahn-Szeg{\"o} inequality, Payne-P{\'o}lya-Weinberger inequality Received: 26 December 2016; Revised: 19 April 2017; Accepted: 19 April 2017 Communicated by Allaberen Ashyralyev This paper was published under project AP05133239 and target program BR05236656 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan. The third author was partially supported by NU SPG grant ”Spectral geometric inequalities in PDE”. Email addresses: [email protected] (Tynysbek Sh. Kal{\textquoteright}menov), [email protected] (Aidyn Kassymov), [email protected] (Durvudkhan Suragan) Publisher Copyright: {\textcopyright} 2018, University of Nis. All rights reserved.",

year = "2018",

month = jan,

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doi = "10.2298/FIL1803885K",

language = "English",

volume = "32",

pages = "885--892",

journal = "Filomat",

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publisher = "Universitet of Nis",

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AU - Kal’menov, Tynysbek Sh

AU - Kassymov, Aidyn

AU - Suragan, Durvudkhan

N1 - Funding Information: 2010 Mathematics Subject Classification. Primary 35P05; Secondary 58J50 Keywords. Cauchy-Dirichlet heat operator, s-number, Rayleigh-Faber-Krahn inequality, Hong-Krahn-Szegö inequality, Payne-Pólya-Weinberger inequality Received: 26 December 2016; Revised: 19 April 2017; Accepted: 19 April 2017 Communicated by Allaberen Ashyralyev This paper was published under project AP05133239 and target program BR05236656 of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan. The third author was partially supported by NU SPG grant ”Spectral geometric inequalities in PDE”. Email addresses: [email protected] (Tynysbek Sh. Kal’menov), [email protected] (Aidyn Kassymov), [email protected] (Durvudkhan Suragan) Publisher Copyright: © 2018, University of Nis. All rights reserved.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in a circular cylinder among all Euclidean cylindric domains of a given measure. It is an analogue of the Rayleigh-Faber-Krahn inequality for the heat operator. We also prove a Hong-Krahn-Szegö and a Payne-Pólya-Weinberger type inequalities for the Cauchy-Dirichlet heat operator.

AB - In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in a circular cylinder among all Euclidean cylindric domains of a given measure. It is an analogue of the Rayleigh-Faber-Krahn inequality for the heat operator. We also prove a Hong-Krahn-Szegö and a Payne-Pólya-Weinberger type inequalities for the Cauchy-Dirichlet heat operator.

KW - Cauchy-Dirichlet heat operator

KW - Hong-Krahn-Szegö inequality

KW - Payne-Pólya-weinberger inequality

KW - Rayleigh-Faber-Krahn inequality

KW - S-number

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Isoperimetric inequalities for the cauchy-dirichlet heat operator

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Keywords

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