Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds
Amongst N-dimensional rectangular parallelepipeds (boxes) of a given volume, that which has the smallest fundamental Robin eigenvalue for the Laplacian is the N -cube. We give an elementary proof of this isoperimetric inequality based on the well-known formulae for the eigenvalues. Also treated are...
| Main Authors: | , |
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| Format: | Journal Article |
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Element d.o.o.
2018
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| Online Access: | http://files.ele-math.com/preprints/mia-21-62.pdf http://hdl.handle.net/20.500.11937/68872 |
| _version_ | 1848761910837641216 |
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| author | Keady, G. Wiwatanapataphee, Benchawan |
| author_facet | Keady, G. Wiwatanapataphee, Benchawan |
| author_sort | Keady, G. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Amongst N-dimensional rectangular parallelepipeds (boxes) of a given volume, that which has the smallest fundamental Robin eigenvalue for the Laplacian is the N -cube. We give an elementary proof of this isoperimetric inequality based on the well-known formulae for the eigenvalues. Also treated are variously related inequalities which are amenable to investigation using the formulae for the eigenvalues. |
| first_indexed | 2025-11-14T10:39:11Z |
| format | Journal Article |
| id | curtin-20.500.11937-68872 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:39:11Z |
| publishDate | 2018 |
| publisher | Element d.o.o. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-688722018-09-06T03:00:04Z Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds Keady, G. Wiwatanapataphee, Benchawan Amongst N-dimensional rectangular parallelepipeds (boxes) of a given volume, that which has the smallest fundamental Robin eigenvalue for the Laplacian is the N -cube. We give an elementary proof of this isoperimetric inequality based on the well-known formulae for the eigenvalues. Also treated are variously related inequalities which are amenable to investigation using the formulae for the eigenvalues. 2018 Journal Article http://hdl.handle.net/20.500.11937/68872 10.7153/mia-2018-21-62 http://files.ele-math.com/preprints/mia-21-62.pdf Element d.o.o. fulltext |
| spellingShingle | Keady, G. Wiwatanapataphee, Benchawan Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds |
| title | Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds |
| title_full | Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds |
| title_fullStr | Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds |
| title_full_unstemmed | Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds |
| title_short | Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds |
| title_sort | inequalities for the fundamental robin eigenvalue for the laplacian on n-dimensional rectangular parallelepipeds |
| url | http://files.ele-math.com/preprints/mia-21-62.pdf http://hdl.handle.net/20.500.11937/68872 |