On S-Number Inequalities of Triangular Cylinders for the Heat Operator

Tynysbek Kal’menov; Aidyn Kassymov; Durvudkhan Suragan

doi:10.1007/978-3-319-67053-9_33

On S-Number Inequalities of Triangular Cylinders for the Heat Operator

Tynysbek Kal’menov, Aidyn Kassymov, Durvudkhan Suragan

Al Farabi Kazakh National University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in the equilateral cylinder among all Euclidean triangular cylindric domains of a given volume as well as we obtain spectral geometric inequalities of the Cauchy-Dirichlet-Neumann heat operator in the right and equilateral triangular cylinder. It is also established that maximum of the second s-number of the Cauchy-Neumann heat operator is reached by the equilateral triangular cylinder among all triangular cylinders of given volume. In addition, we prove that the second s-number of the Cauchy-Neumann heat operator is maximized in the circular cylinder among all cylindrical Lipschitz domains of fixed volume.

Original language	English
Title of host publication	Functional Analysis in Interdisciplinary Applications
Editors	Erlan D. Nursultanov, Tynysbek Sh. Kalmenov, Makhmud A. Sadybekov, Michael V. Ruzhansky
Publisher	Springer New York
Pages	349-362
Number of pages	14
Volume	216
ISBN (Print)	9783319670522
DOIs	https://doi.org/10.1007/978-3-319-67053-9_33
Publication status	Published - Jan 1 2017
Externally published	Yes
Event	International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017 - Astana, Kazakhstan Duration: Oct 2 2017 → Oct 5 2017

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	216
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017
Country/Territory	Kazakhstan
City	Astana
Period	10/2/17 → 10/5/17

Keywords

Heat operator
Isoperimetric inequalities
Non-selfadjoint operator
Polya inequality
S-Number

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-67053-9_33

Cite this

Kal’menov, T., Kassymov, A., & Suragan, D. (2017). On S-Number Inequalities of Triangular Cylinders for the Heat Operator. In E. D. Nursultanov, T. S. Kalmenov, M. A. Sadybekov, & M. V. Ruzhansky (Eds.), Functional Analysis in Interdisciplinary Applications (Vol. 216, pp. 349-362). (Springer Proceedings in Mathematics and Statistics; Vol. 216). Springer New York. https://doi.org/10.1007/978-3-319-67053-9_33

On S-Number Inequalities of Triangular Cylinders for the Heat Operator. / Kal’menov, Tynysbek; Kassymov, Aidyn; Suragan, Durvudkhan.
Functional Analysis in Interdisciplinary Applications. ed. / Erlan D. Nursultanov; Tynysbek Sh. Kalmenov; Makhmud A. Sadybekov; Michael V. Ruzhansky. Vol. 216 Springer New York, 2017. p. 349-362 (Springer Proceedings in Mathematics and Statistics; Vol. 216).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kal’menov, T, Kassymov, A & Suragan, D 2017, On S-Number Inequalities of Triangular Cylinders for the Heat Operator. in ED Nursultanov, TS Kalmenov, MA Sadybekov & MV Ruzhansky (eds), Functional Analysis in Interdisciplinary Applications. vol. 216, Springer Proceedings in Mathematics and Statistics, vol. 216, Springer New York, pp. 349-362, International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017, Astana, Kazakhstan, 10/2/17. https://doi.org/10.1007/978-3-319-67053-9_33

Kal’menov, Tynysbek ; Kassymov, Aidyn ; Suragan, Durvudkhan. / On S-Number Inequalities of Triangular Cylinders for the Heat Operator. Functional Analysis in Interdisciplinary Applications. editor / Erlan D. Nursultanov ; Tynysbek Sh. Kalmenov ; Makhmud A. Sadybekov ; Michael V. Ruzhansky. Vol. 216 Springer New York, 2017. pp. 349-362 (Springer Proceedings in Mathematics and Statistics).

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abstract = "In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in the equilateral cylinder among all Euclidean triangular cylindric domains of a given volume as well as we obtain spectral geometric inequalities of the Cauchy-Dirichlet-Neumann heat operator in the right and equilateral triangular cylinder. It is also established that maximum of the second s-number of the Cauchy-Neumann heat operator is reached by the equilateral triangular cylinder among all triangular cylinders of given volume. In addition, we prove that the second s-number of the Cauchy-Neumann heat operator is maximized in the circular cylinder among all cylindrical Lipschitz domains of fixed volume.",

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N2 - In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in the equilateral cylinder among all Euclidean triangular cylindric domains of a given volume as well as we obtain spectral geometric inequalities of the Cauchy-Dirichlet-Neumann heat operator in the right and equilateral triangular cylinder. It is also established that maximum of the second s-number of the Cauchy-Neumann heat operator is reached by the equilateral triangular cylinder among all triangular cylinders of given volume. In addition, we prove that the second s-number of the Cauchy-Neumann heat operator is maximized in the circular cylinder among all cylindrical Lipschitz domains of fixed volume.

AB - In this paper we prove that the first s-number of the Cauchy-Dirichlet heat operator is minimized in the equilateral cylinder among all Euclidean triangular cylindric domains of a given volume as well as we obtain spectral geometric inequalities of the Cauchy-Dirichlet-Neumann heat operator in the right and equilateral triangular cylinder. It is also established that maximum of the second s-number of the Cauchy-Neumann heat operator is reached by the equilateral triangular cylinder among all triangular cylinders of given volume. In addition, we prove that the second s-number of the Cauchy-Neumann heat operator is maximized in the circular cylinder among all cylindrical Lipschitz domains of fixed volume.

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On S-Number Inequalities of Triangular Cylinders for the Heat Operator

Abstract

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Keywords

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