Asymptotic analysis of a mixed boundary value problem in a multi-structure
Vladimir Arkad'evich Kozlov, Vladimir Gilelevich Maz'ya, A. B. Movchan · Asymptotic Analysis · 1994
We consider a mixed boundary value problem for the Laplace operator in a union of a three-dimensional domain and thin cylinders. A rigorous procedure is developed to derive the total asymptotic expansion. The asymptotic formulae for the first eigenvalue and corresponding eigenfunction have been obtained.