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Displaying similar documents to “On the solution of the Liouville equation over a rectangle.”

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.

Lower and upper bounds for the Rayleigh conductivity of a perforated plate

S. Laurens, S. Tordeux, A. Bendali, M. Fares, P. R. Kotiuga (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational...