UNIVERSAL INEQUALITIES FOR EIGENVALUES OF THE VIBRATION PROBLEM FOR A CLAMPED PLATE ON RIEMANNIAN MANIFOLDS

2009 ◽  
Vol 62 (1) ◽  
pp. 235-258 ◽  
Author(s):  
C. Xia
Keyword(s):  
Riemannian Manifolds ◽  
Clamped Plate ◽  
Vibration Problem ◽  
Universal Inequalities

Universal inequalities for a horizontal Laplacian version of the clamped plate problem on Carnot group

2017 ◽  
Vol 37 (5) ◽  
pp. 1536-1544
Author(s):  
Feng DU ◽  
Chuanxi WU ◽  
Guanghan LI ◽  
Changyu XIA
Keyword(s):  
Carnot Group ◽  
Clamped Plate ◽  
Universal Inequalities

Upper Spectral Bound of Biharmonic Operator Eigenvalue Problem by Bicubic Hermite Element

2012 ◽  
Vol 466-467 ◽  
pp. 430-434
Author(s):  
Shi Xian Ren ◽  
Yi Du Yang ◽  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
Upper Bound ◽  
Biharmonic Operator ◽  
Clamped Plate ◽  
Spectral Bound ◽  
Vibration Problem ◽  
Morley Element ◽  
Matlab Program

This paper uses the bicubic Hermite element to compute the first four eigenvalues of the vibration problem of clamped plate by Matlab program and gives upper bound of the exact eigenvalues. Combing Matlab experiments on Morley element for lower spectral bound we can provide a range of the exact eigenvalues of biharmonic operator more accurately.

scholarly journals Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on Riemannian Manifolds

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Shenyang Tan ◽  
Tiren Huang ◽  
Wenbin Zhang
Keyword(s):  
Elliptic Operator ◽  
Riemannian Manifolds ◽  
Special Functions ◽  
Type Inequality ◽  
Divergence Form ◽  
Hadamard Manifolds ◽  
Complete Submanifolds ◽  
Universal Inequalities ◽  
Complete Manifolds ◽  
Bounded Below

We investigate the Dirichlet weighted eigenvalue problem of the elliptic operator in divergence form on compact Riemannian manifolds(M,g,e-ϕdv). We establish a Yang-type inequality of this problem. We also get universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below and any complete manifolds admitting eigenmaps to a sphere.

scholarly journals Estimates for eigenvalues of a clamped plate problem on Riemannian manifolds

2010 ◽  
Vol 62 (2) ◽  
pp. 673-686 ◽  
Author(s):  
Qing-Ming CHENG ◽  
Takamichi ICHIKAWA ◽  
Shinji MAMETSUKA
Keyword(s):  
Riemannian Manifolds ◽  
Clamped Plate

EIGENVALUE ESTIMATES ON DOMAIN OF THE POLYDISK

2012 ◽  
Vol 23 (01) ◽  
pp. 1250014
Author(s):  
TAO ZHENG ◽  
DAGUANG CHEN ◽  
MIN CAI
Keyword(s):  
Bounded Domain ◽  
First Eigenvalue ◽  
Dirichlet Laplacian ◽  
Clamped Plate ◽  
Eigenvalue Estimates ◽  
The First Eigenvalue ◽  
Universal Inequalities

In this paper, we investigate universal inequalities for eigenvalues of the Dirichlet Laplacian and the clamped plate problem on a bounded domain in an n-dimensional polydisk 𝔻n. Moreover, from the domain monotonicity of the eigenvalue, we can prove that if the first eigenvalue of the Dirichlet Laplacian tends to [Formula: see text] when the domain tends to the polydisk 𝔻n, then all of the eigenvalues tend to [Formula: see text].

On the equicontinuity of families of inverse mappings of Riemannian manifolds

2019 ◽  
Vol 16 (4) ◽  
pp. 557-566
Author(s):  
Denis Ilyutko ◽  
Evgenii Sevost'yanov
Keyword(s):  
Riemannian Manifolds ◽  
Type Inequality ◽  
The Given ◽  
Range Of Values

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

Sign in / Sign up

Export Citation Format

Share Document