Namlyeyeva Y. The eigenvalues of variation elliptic problems in perforated domains

3. The dissertation is devoted to the question of homogenization of the families of Dirichlet eigenvalue problem for elliptic second order and higher order equations in perforated domains of different structure. The convergence of the eigenvalues and eigenfunctions of Dirichlet problems for linear and nonlinear elliptic second order equations in a family of domains with a finely granulated boundary to the corresponding eigenvalues and eigenfunctions of the Dirichlet problems for equations with capacity terms is proved. The behavior of the eigenfunctions and eigenvalues of the Dirichlet problems for second order and higher order equations in perforated domains of general structure is studied.