Asymptotics for eigenvalues of the Laplacian with a Neumann boundary condition on a thin cut-out tube
M. Yu. Planida · Comptes Rendus Mécanique · 2003
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.