We investigate the behaviour of a sequence $λ_{s}$, s = 1,2,..., of eigenvalues of the Dirichlet problem for the p-Laplacian in the domains $Ω_{s}$, s = 1,2,..., obtained by removing from a given domain Ω a set $E_{s}$ whose diameter vanishes when s → ∞. We estimate the deviation of $λ_{s}$ from the eigenvalue of the limit problem. For the derivation of our results we construct an appropriate asymptotic expansion for the sequence of solutions of the original eigenvalue problem.
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We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains $Q_{T}^{(s)}$, s = 1,2,... We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of $Q_{T}^{(s)}$. We give an explicit construction of that limit problem.
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