Asymptotics of the eigenvalues of boundary value problems for the Laplace operator in a three-dimensional domain with a thin closed tube (Q2788919)

Spectral asymptotic properties for several boundary value problems are studied. These problems involve the Laplace operator in three-dimensional singularly perturbed domains \(\Omega (\varepsilon) = \Omega \setminus \overline{\Gamma}_{\varepsilon}\) with a thin cavity \(\Gamma_{\varepsilon}\). Mixed boundary value problems with the Neumann conditions on \( \partial \Gamma_{\varepsilon}\) and also spectral problems with lumped masses on \(\Gamma_{\varepsilon}\) are considered.