Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tubeComportement asymptotique des valeurs propres du laplacien avec conditions de Neumann sur un tube extrait

We consider the eigenvalue problem for the Laplace operator in a bounded three-dimensional domain where a thin tube is cut out. Imposing a Neumann boundary condition on the boundary of this tube, we construct asymptotics for eigenvalues on the small parameter that is a diameter of the tube. To cite this article: M.Yu. Planida, C. R. Mecanique 331 (2003).