Geodesic
Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 648-676 Cet article a éte moissonné depuis la source Numdam

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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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     title = {Bounds for the first {Dirichlet} eigenvalue of triangles and quadrilaterals},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {648--676},
     year = {2010},
     publisher = {EDP-Sciences},
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     zbl = {1205.35174},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009018/}
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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, Tome 16 (2010) no. 3, pp. 648-676. doi: 10.1051/cocv/2009018

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