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

Tynysbek Kal’menov, Aidyn Kassymov, Durvudkhan Suragan

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationFunctional Analysis in Interdisciplinary Applications
EditorsErlan D. Nursultanov, Tynysbek Sh. Kalmenov, Makhmud A. Sadybekov, Michael V. Ruzhansky
PublisherSpringer New York
Pages349-362
Number of pages14
Volume216
ISBN (Print)9783319670522
DOIs
Publication statusPublished - Jan 1 2017
Externally publishedYes
EventInternational Conference on Functional analysis in interdisciplinary applications, FAIA 2017 - Astana, Kazakhstan
Duration: Oct 2 2017Oct 5 2017

Conference

ConferenceInternational Conference on Functional analysis in interdisciplinary applications, FAIA 2017
CountryKazakhstan
CityAstana
Period10/2/1710/5/17

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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