Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

Giuseppe Cardone; Sergey A. Nazarov; Jan Sokolowski; Jari Taskinen

doi:10.1016/j.crme.2007.10.001

Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain
[Développements asymptotiques des solutions harmoniques d'un problème de Neumann lorsqu'une cavité est proche d'un bord extérieur du domaine]

Présenté par : Évariste Sanchez-Palencia

Giuseppe Cardone ¹ ; Sergey A. Nazarov ² ; Jan Sokolowski ³ ; Jari Taskinen ⁴

¹ Università del Sannio, Dipartimento di Ingegneria, Piazza Roma, 21, 84100 Benevento, Italy
² Institute of Mechanical Engineering Problems, V.O., Bolshoi pr. 61, 199178 St. Petersburg, Russia
³ Université Henri-Poincaré, Nancy 1, département de mathematiques, B.P. 239, 54506 Vandoeuvre les Nancy cedex, France
⁴ University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, 00014 Helsinki, Finland

Comptes Rendus. Mécanique, Volume 335 (2007) no. 12, pp. 763-767.

Résumé
Abstract

Nous construisons les développements asymptotiques (lorsque ε tend vers 0) des solutions d'un problème de Neumann pour l'équation de Laplace ainsi que le développement asymptotique de l'intégrale de Dirichlet correspondante. Le problème est défini dans un domaine tri-dimensionnel avec un bord ayant deux composantes connexes distantes de $ε > 0$ .

We construct the asymptotics (as $ε \to 0$ ) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance $ε > 0$ .

Reçu le : 2007-09-25
Accepté le : 2007-10-02
Publié le : 2007-11-08

DOI : 10.1016/j.crme.2007.10.001

Keywords: Singularly perturbed Neumann problem, Touching surfaces, Dirichlet integral, Thin ligament
Mot clés : Problème singularement perturbé, Surfaces en contact, Integrale Dirichlet, Ligament fin

Affiliations des auteurs :

Giuseppe Cardone ¹ ; Sergey A. Nazarov ² ; Jan Sokolowski ³ ; Jari Taskinen ⁴

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     title = {Asymptotics of {Neumann} harmonics when a cavity is close to the exterior boundary of the domain},
     journal = {Comptes Rendus. M\'ecanique},
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Giuseppe Cardone; Sergey A. Nazarov; Jan Sokolowski; Jari Taskinen. Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain. Comptes Rendus. Mécanique, Volume 335 (2007) no. 12, pp. 763-767. doi : 10.1016/j.crme.2007.10.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.10.001/

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