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

Fractional Calculus and Applied Analysis (2005)

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

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topKhelifi, 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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