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 language | English |
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Title of host publication | Functional Analysis in Interdisciplinary Applications |
Editors | Erlan D. Nursultanov, Tynysbek Sh. Kalmenov, Makhmud A. Sadybekov, Michael V. Ruzhansky |
Publisher | Springer New York |
Pages | 349-362 |
Number of pages | 14 |
Volume | 216 |
ISBN (Print) | 9783319670522 |
DOIs | |
Publication status | Published - Jan 1 2017 |
Externally published | Yes |
Event | International Conference on Functional analysis in interdisciplinary applications, FAIA 2017 - Astana, Kazakhstan Duration: Oct 2 2017 → Oct 5 2017 |
Conference
Conference | International Conference on Functional analysis in interdisciplinary applications, FAIA 2017 |
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Country | Kazakhstan |
City | Astana |
Period | 10/2/17 → 10/5/17 |
Keywords
- Heat operator
- Isoperimetric inequalities
- Non-selfadjoint operator
- Polya inequality
- S-Number
ASJC Scopus subject areas
- Mathematics(all)