Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 648-676.

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.

DOI: 10.1051/cocv/2009018
Classification: 35P15, 35J05
Keywords: Dirichlet eigenvalues, polygons, variational bounds
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Freitas, Pedro; Siudeja, Batłomiej. Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 648-676. doi : 10.1051/cocv/2009018. http://archive.numdam.org/articles/10.1051/cocv/2009018/

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