A boundary integral method. Application to the Laplacian and to elasticity.

Marie-Thérèse Lacroix

Revista Matemática de la Universidad Complutense de Madrid (1991)

  • Volume: 4, Issue: 2-3, page 265-278
  • ISSN: 1139-1138

Abstract

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The aim of the paper is to give a method to solve boundary value problems associated to the Helmholtz equation and to the operator of elasticity. We transform these problems in problems on the boundary Gamma of an open set of R3. After introducing a symplectic form on H1,2(G) x H-1,2(G) we obtain the adjoint of the boundary operator employed. Then the boundary problem has a solution if and only if the boundary conditions are orthogonal, for this bilinear form, to the elements of the kernel, in a good space, of the adjoint operator. We illustrate this result for a mixed problem for the Helmholtz equation (th. II.3) and the Dirichlet problem for elasticity (th. III.2), but there exist natural generalizations.

How to cite

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Lacroix, Marie-Thérèse. "Une méthode intégrale de frontière. Application au Laplacien et à l'élasticité.." Revista Matemática de la Universidad Complutense de Madrid 4.2-3 (1991): 265-278. <http://eudml.org/doc/44314>.

@article{Lacroix1991,
author = {Lacroix, Marie-Thérèse},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Problemas de valor de frontera; Operador laplaciano; Elasticidad; Ecuación de Helmholtz; boundary value problems; Helmholtz equation; mixed problem; Dirichlet problem},
language = {fre},
number = {2-3},
pages = {265-278},
title = {Une méthode intégrale de frontière. Application au Laplacien et à l'élasticité.},
url = {http://eudml.org/doc/44314},
volume = {4},
year = {1991},
}

TY - JOUR
AU - Lacroix, Marie-Thérèse
TI - Une méthode intégrale de frontière. Application au Laplacien et à l'élasticité.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1991
VL - 4
IS - 2-3
SP - 265
EP - 278
LA - fre
KW - Problemas de valor de frontera; Operador laplaciano; Elasticidad; Ecuación de Helmholtz; boundary value problems; Helmholtz equation; mixed problem; Dirichlet problem
UR - http://eudml.org/doc/44314
ER -

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