scholarly journals Strict inequality of Robin eigenvalues for elliptic differential operators on Lipschitz domains

2014 ◽  
Vol 418 (2) ◽  
pp. 978-984 ◽  
Author(s):  
Jonathan Rohleder
Keyword(s):  
Differential Operators ◽  
Strict Inequality ◽  
Lipschitz Domains ◽  
Elliptic Differential Operators

Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators

2021 ◽  
pp. 1-16
Author(s):  
Alexander Dabrowski
Keyword(s):  
General Type ◽  
Differential Operators ◽  
Laplacian Operator ◽  
Variational Characterization ◽  
Repeated Eigenvalues ◽  
Direct Extension ◽  
Asymptotic Formulae ◽  
Elliptic Differential Operators ◽  
Domain Perturbations ◽  
Boundary Deformation

A variational characterization for the shift of eigenvalues caused by a general type of perturbation is derived for second order self-adjoint elliptic differential operators. This result allows the direct extension of asymptotic formulae from simple eigenvalues to repeated ones. Some examples of particular interest are presented theoretically and numerically for the Laplacian operator for the following domain perturbations: excision of a small hole, local change of conductivity, small boundary deformation.

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

scholarly journals The approximation of the solution of wave problems by spectral expansions connected with elliptic differential operators

2021 ◽  
Vol 86 (2) ◽  
pp. 101-106
Author(s):  
Abdulkasim Akhmedov ◽  
Mohd Zuki Salleh ◽  
Abdumalik Rakhimov
Keyword(s):  
Wave Propagation ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Elastic Membrane ◽  
Conductive Material ◽  
Spectral Expansions ◽  
Vibration Process ◽  
Thermally Conductive ◽  
Elliptic Differential Operators ◽  
Wave Problems

In this research, we investigate the spectral expansions connected with elliptic differential operators in the space of singular distributions, which describes the vibration process made of thin elastic membrane stretched tightly over a circular frame. The sufficient conditions for summability of the spectral expansions connected with wave problems on the disk are obtained by taking into account that the deflection of the membrane during the motion remains small compared to the size of the membrane and for wave propagation problems, the disk is made of some thermally conductive material.

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