IJPAM: Volume 113, No. 4 (2017)
TitlePOLYA TYPE INEQUALITIES FOR
THE HEAT OPERATOR IN POLYGONAL CYLINDERS
AuthorsTynysbek Sh. Kalmenov, Aidyn Kassymov, Durvudkhan Suragan
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University
AbstractIn 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 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.
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, -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
Pages: 65 - 70
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