| Issue |
ESAIM: COCV
Volume 16, Number 3, July-September 2010
|
|
|---|---|---|
| Page(s) | 648 - 676 | |
| DOI | https://doi.org/10.1051/cocv/2009018 | |
| Published online | 02 July 2009 | |
Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
1
Department of Mathematics, Faculdade de Motricidade Humana (TU Lisbon) and
Group of Mathematical Physics of the University of Lisbon, Complexo Interdisciplinar,
Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal. freitas@cii.fc.ul.pt
2
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. siudeja@illinois.edu
Received:
18
September
2008
Revised:
5
March
2009
We prove some new upper and lower bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. In particular, we improve Pólya and Szegö's [Annals of Mathematical Studies 27 (1951)] lower bound for quadrilaterals and extend Hersch's [Z. Angew. Math. Phys. 17 (1966) 457–460] upper bound for parallelograms to general quadrilaterals.
Mathematics Subject Classification: 35P15 / 35J05
Key words: Dirichlet eigenvalues / polygons / variational bounds
© EDP Sciences, SMAI, 2009
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