Titlebook: General Inequalities 7; 7th International Co Catherine Bandle,William N. Everitt,Wolfgang Walte Conference proceedings 1997 Springer Basel

Adulate

Discontinuous dependence of the ,-th Sturm-Liouville eigenvalueThe .-th eigenvalue of a regular Sturm-Liouville problem is not a continuous function of the boundary conditions. On the other hand if the index . is allowed to “jump”, then each eigenvalue can be embedded in an eigenvalue “branch” which is not only continuous but differentiable.

不幸的人

Note on Wirtinger’s inequalityIn this note we refine the following theorem due to W. Wirtinger: If . has period 2π and satisfies ., then . with strict inequality unless .(.) = . cos(.) + . sin(.), (., . ∈ ?).

邊緣

Opial-type inequalities involving higher order partial derivatives of two functionsIn this paper we offer very general Opial-type inequalities involving higher order partial derivatives of two functions of two independent variables. From these inequalities we then deduce extended and improved versions of several recent results.

印第安人

The HELP type integral inequalities for 2,, order differential operatorsIn 1971 W.N. Everitt published his seminal work on the family of HELP inequalities. This paper, written in the twenty-fifth year of the HELP paper, is respectfully dedicated to him.

grenade

泥瓦匠

噴油井

Inequalities for the first eigenvalues of the clamped plate and buckling problemse was finally proved by Nadirashvili in 1992, with important earlier contributions due to Szeg? and Talenti. An analogous conjecture concerning the critical buckling load of a clamped plate was made by Pólya and Szeg? around 1950. This conjecture remains open. This paper surveys the state of our kno

PRE

On the Payne-Pólya-Weinberger conjecture on the ,-dimensional sphere of its first two Dirichlet eigenvalues where Ω*, the symmetric rearrangement of Ω in .., is a geodesic ball in .. having the same .-volume as Ω. Along the way we show that λ./λ. for geodesic balls of geodesic radius .. less than or equal to π/2 is an increasing function of ... Our key result is tha

閑逛

Sedative

https://doi.org/10.1007/978-3-662-06297-5 specific choices of the weights one obtains the .-dimensional Hardy inequalities whose constants are sharp and independent of ...In addition a gradient inequality and an exponential integral inequality is characterized in terms of the weight functions.