Nitsch, Carlo 
ORCID: 0000-0001-6673-9332
(2014).
ON THE FIRST DIRICHLET LAPLACIAN EIGENVALUE OF REGULAR POLYGONS.
Kodai. Math. J., 37 (3).
S. 595 - 608.
TOKYO:
KINOKUNIYA CO LTD.
ISSN 0386-5991
Abstract
The Faber-Krahn inequality in R-2 states that among all open bounded sets of given area the disk minimizes the first Dirichlet Laplacian eigenvalue. It was conjectured in [1] that for all N >= 3 the first Dirichlet Laplacian eigenvalue of the regular N-gon is greater than the one of the regular (N + 1)-gon of same area. This natural idea is suggested by the fact that the shape becomes more and more rounded as N increases and it is supported by clear numerical evidences. Aiming to settle such a conjecture, in this work we investigate possible ways to estimate the difference between eigenvalues of regular N-gons and (N + 1)-gons.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-426291 | ||||||||
| DOI: | 10.2996/kmj/1414674611 | ||||||||
| Journal or Publication Title: | Kodai. Math. J. | ||||||||
| Volume: | 37 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | S. 595 - 608 | ||||||||
| Date: | 2014 | ||||||||
| Publisher: | KINOKUNIYA CO LTD | ||||||||
| Place of Publication: | TOKYO | ||||||||
| ISSN: | 0386-5991 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| URI: | http://kups.ub.uni-koeln.de/id/eprint/42629 |
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