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Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals

Published online by Cambridge University Press:  02 July 2009

Pedro Freitas  and
Batłomiej Siudeja
Pedro Freitas
Affiliation:
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
Batłomiej Siudeja
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. siudeja@illinois.edu
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Abstract

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.

Keywords

Dirichlet eigenvaluespolygonsvariational bounds
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 3 , July 2010 , pp. 648 - 676
Copyright
© EDP Sciences, SMAI, 2009

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References

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