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.
Mots-clés : Dirichlet eigenvalues, polygons, variational bounds
@article{COCV_2010__16_3_648_0,
author = {Freitas, Pedro and Siudeja, Bat{\l}omiej},
title = {Bounds for the first {Dirichlet} eigenvalue of triangles and quadrilaterals},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {648--676},
publisher = {EDP-Sciences},
volume = {16},
number = {3},
year = {2010},
doi = {10.1051/cocv/2009018},
mrnumber = {2674631},
zbl = {1205.35174},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009018/}
}
TY - JOUR AU - Freitas, Pedro AU - Siudeja, Batłomiej TI - Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 648 EP - 676 VL - 16 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009018/ DO - 10.1051/cocv/2009018 LA - en ID - COCV_2010__16_3_648_0 ER -
%0 Journal Article %A Freitas, Pedro %A Siudeja, Batłomiej %T Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 648-676 %V 16 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009018/ %R 10.1051/cocv/2009018 %G en %F COCV_2010__16_3_648_0
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. http://www.numdam.org/articles/10.1051/cocv/2009018/
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