New bounds for the principal Dirichlet eigenvalue of planar regions.
Antunes, Pedro, Freitas, Pedro (2006)
Experimental Mathematics
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Displaying similar documents to “Fundamental tones and buckling loads of clamped plates”
New bounds for the principal Dirichlet eigenvalue of planar regions.
When is the first eigenfunction for the clamped plate equation of fixed sign?
Sweers, Guido (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Approximation of eigenvalues and a Koehler's type method
Cesare Davini (1982)
Rendiconti del Seminario Matematico della Università di Padova
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Asymptotics of the first nodal line
Daniel Grieser, David Jerison (1995)
Journées équations aux dérivées partielles
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A counterexample to the “hot spots" conjecture.
Burdzy, Krzysztof, Werner, Wendelin (1999)
Annals of Mathematics. Second Series
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Perturbation of a biharmonic eigenvalue problem
Zaman, F.D. (1977)
Portugaliae mathematica
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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.