IJPAM: Volume 113, No. 4 (2017)

Title

POLYA TYPE INEQUALITIES FOR
THE HEAT OPERATOR IN POLYGONAL CYLINDERS

Authors

Tynysbek Sh. Kalmenov$^1$, Aidyn Kassymov$^2$, Durvudkhan Suragan$^3$
$^{1,2,3}$Institute of Mathematics and Mathematical Modeling
Almaty, KAZAKHSTAN
$^2$Al-Farabi Kazakh National University
Almaty, KAZAKHSTAN

Abstract

In this note we prove Polya type inequalities for the Cauchy-Dirichlet heat operator in polygonal cylindric domains of a given volume. That is, in particular, we prove that the $s_{1}-$number of the Cauchy-Dirichlet heat operator is minimized in the equilateral triangular cylinder among all triangular cylinders of given volume, which means that the operator norm of the inverse operator is maximized in the equilateral triangular cylinder among all triangular cylinders of a given volume.

History

Received: December 15, 2016
Revised: January 30, 2017
Published: March 30, 2017

AMS Classification, Key Words

AMS Subject Classification: 35P05, 58J50
Key Words and Phrases: heat operator, $s$-numbers, Polya inequality

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How to Cite?

DOI: 10.12732/ijpam.v113i4.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 4
Pages: 65 - 70


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