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
Full text not available from this repository.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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