Volume 16, Number 3, July-September 2010
|Page(s)||648 - 676|
|Published online||02 July 2009|
Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
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. email@example.com
2 Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. firstname.lastname@example.org
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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