Some inequalities between Dirichlet and neumann eigenvalues

Friedlander, Leonid

doi:10.1007/bf00375590

Cited by 124 publications

(131 citation statements)

References 5 publications

Supporting

Mentioning

126

Contrasting

Order By: Relevance

“…Levine and Weinberger also established various extensions to nonsmooth domains, including the result ^+n-i ^ A^ for all k ^ 1 for an arbitrary bounded convex domain in R 71 . To complete the story, we remark that relatively recently Friedlander [11] was able to establish Payne's conjecture (1.6) in the strict form…”

Section: B Euclidean Case: General Resultsmentioning

confidence: 96%

Inequalities for Dirichlet and Neumann eingenvalues of the laplacian for domains on spheres

Ashbaugh¹,

Levine²

1997

Journées Équations Aux Dérivées Partielles

View full text Add to dashboard Cite

Section: B Euclidean Case: General Resultsmentioning

confidence: 96%

Inequalities for Dirichlet and Neumann eingenvalues of the laplacian for domains on spheres

Ashbaugh¹,

Levine²

1997

Journées Équations Aux Dérivées Partielles

View full text Add to dashboard Cite

“…The ultrasonic wave propagates along y-axis. Neumann boundary condition [20][21][22] is employed for the interface between the ultrasonic transducer and the steel. For time-harmonic displacementû(x, t) = exp(−iωt)u(x) with an angular frequency ω and imaginary unit i = √ −1, the timeharmonic waves in a domain Ω can be described by a Navier equation…”

Section: Fig 1 Principle Of Boundary Condition Excitationmentioning

confidence: 99%

Ultrasonic beam steering using Neumann boundary condition in multiplysics

Zhaoguo

2012

Acta Mech Sin

View full text Add to dashboard Cite

The traditional one-dimensional ultrasonic beam steering has time delay and is thus a complicated problem. A numerical model of ultrasonic beam steering using Neumann boundary condition in multiplysics is presented in the present paper. This model is based on the discrete wave number method that has been proved theoretically to satisfy the continuous conditions. The propagating angle of novel model is a function of the distance instead of the time domain. The propagating wave fronts at desired angles are simulated with the single line sources for plane wave. The result indicates that any beam angle can be steered by discrete line elements resources without any time delay.

show abstract

“…This question was settled by Friedlander [28] in 1991 for domains with smooth boundaries. More recently, Friedlander's breakthrough was generalized for domains with non-smooth boundaries by Filonov [27].…”

Section: Four New Estimatesmentioning

confidence: 99%