Journal of Mathematical Sciences

, Volume 75, Issue 3, pp 1715–1749 | Cite as

Asymptotics of solutions of boundary value problems in periodically perforated domains with small holes

  • A. G. Belyaev


We consider boundary value problems for operators Δ and Δ2 in periodically perforated domains with homogeneous Dirichlet conditions on the boundaries of the holes. The period of perforation and the “size” of the hole with respect to the period of perforation are regarded as two small parameters. We study asymptotic behavior of solutions, eigenvalues, and eigenfunctions for boundary value problems, under various assumptions on the relation between the two parameters. Bibliography: 13 titles.


Perforation Asymptotic Behavior Small Parameter Small Hole Dirichlet Condition 
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© Plenum Publishing Corporation 1995

Authors and Affiliations

  • A. G. Belyaev

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