Comptes Rendus
no. 12
Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

Presented by: Évariste Sanchez-Palencia

Giuseppe Cardone1; Sergey A. Nazarov2; Jan Sokolowski3 ; Jari Taskinen4
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.

We construct the asymptotics (as ε→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.

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.

Received:
Accepted:
Published online:
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

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 
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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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