Abstract: We consider a two-dimensional eigenvalue problem for Laplace
operator with frequent alternation of the boundary-condition type. We study the
cases of the averaged problem with the Dirichlet, Neumann, or Robin
boundary condition. In the case of the circle and a periodic alternation of the
boundary-condition type the complete two-parametrical asymptotics for the eigen-elements
of the problem under consideration is constructed. For an arbitrary domain and
a quasiperiodic alternation we obtain the leading terms of the
asymptotics for the eigen-elements.
In the case of a non-periodical alternation and any domain we derive
estimates for the eigenvalues and give the conditions under those the
leading terms of the asymptotics for the eigen-elements can be
constructed.
