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Published in:
2017 | OriginalPaper | Chapter
On S-Number Inequalities of Triangular Cylinders for the Heat Operator
Authors : Tynysbek Kal’menov, Aidyn Kassymov, Durvudkhan Suragan
Published in: Functional Analysis in Interdisciplinary Applications
Publisher: Springer International Publishing
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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.