Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

Khelifi, Abdessatar

Fractional Calculus and Applied Analysis (2005)

  • Volume: 8, Issue: 3, page 277-298
  • ISSN: 1311-0454

Abstract

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2000 Mathematics Subject Classification: 35J05, 35C15, 44P05In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We derive recursive formulas for the Taylor coefficients of the eigenvalues as functions of the shape-perturbation parameter and we establish the existence of a set of eigenfunctions that is jointly holomorphic in the spatial and boundary-variation variables. Using integral equations, we show that these eigenvalues are exactly built with the characteristic values of some meromorphic operator-valued functions.

How to cite

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Khelifi, Abdessatar. "Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary." Fractional Calculus and Applied Analysis 8.3 (2005): 277-298. <http://eudml.org/doc/11297>.

@article{Khelifi2005,
abstract = {2000 Mathematics Subject Classification: 35J05, 35C15, 44P05In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We derive recursive formulas for the Taylor coefficients of the eigenvalues as functions of the shape-perturbation parameter and we establish the existence of a set of eigenfunctions that is jointly holomorphic in the spatial and boundary-variation variables. Using integral equations, we show that these eigenvalues are exactly built with the characteristic values of some meromorphic operator-valued functions.},
author = {Khelifi, Abdessatar},
journal = {Fractional Calculus and Applied Analysis},
keywords = {35J05; 35C15; 44P05},
language = {eng},
number = {3},
pages = {277-298},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary},
url = {http://eudml.org/doc/11297},
volume = {8},
year = {2005},
}

TY - JOUR
AU - Khelifi, Abdessatar
TI - Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary
JO - Fractional Calculus and Applied Analysis
PY - 2005
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 8
IS - 3
SP - 277
EP - 298
AB - 2000 Mathematics Subject Classification: 35J05, 35C15, 44P05In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We derive recursive formulas for the Taylor coefficients of the eigenvalues as functions of the shape-perturbation parameter and we establish the existence of a set of eigenfunctions that is jointly holomorphic in the spatial and boundary-variation variables. Using integral equations, we show that these eigenvalues are exactly built with the characteristic values of some meromorphic operator-valued functions.
LA - eng
KW - 35J05; 35C15; 44P05
UR - http://eudml.org/doc/11297
ER -

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