TY - GEN

T1 - On S-Number Inequalities of Triangular Cylinders for the Heat Operator

AU - Kal’menov, Tynysbek

AU - Kassymov, Aidyn

AU - Suragan, Durvudkhan

N1 - Publisher Copyright:
© 2017, Springer International Publishing AG.

PY - 2017/1/1

Y1 - 2017/1/1

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.

KW - Heat operator

KW - Isoperimetric inequalities

KW - Non-selfadjoint operator

KW - Polya inequality

KW - S-Number

UR - http://www.scopus.com/inward/record.url?scp=85041373028&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041373028&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-67053-9_33

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

M3 - Conference contribution

AN - SCOPUS:85041373028

SN - 9783319670522

VL - 216

T3 - Springer Proceedings in Mathematics and Statistics

SP - 349

EP - 362

BT - Functional Analysis in Interdisciplinary Applications

A2 - Nursultanov, Erlan D.

A2 - Kalmenov, Tynysbek Sh.

A2 - Sadybekov, Makhmud A.

A2 - Ruzhansky, Michael V.

PB - Springer New York

T2 - International Conference on Functional analysis in interdisciplinary applications, FAIA 2017

Y2 - 2 October 2017 through 5 October 2017

ER -