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Displaying similar documents to “Fundamental tones and buckling loads of clamped plates”

Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals

Pedro Freitas, Batłomiej Siudeja (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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 [  (1951)] lower bound for quadrilaterals and extend Hersch's [  (1966) 457–460] upper bound for parallelograms to general quadrilaterals.

Recent results on Lieb-Thirring inequalities

Ari Laptev, Timo Weidl (2000)

Journées équations aux dérivées partielles

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We give a survey of results on the Lieb-Thirring inequalities for the eigenvalue moments of Schrödinger operators. In particular, we discuss the optimal values of the constants therein for higher dimensions. We elaborate on certain generalisations and some open problems as well.