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Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole

M. Sango — 2001

Colloquium Mathematicae

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.

Asymptotic analysis of the initial boundary value problem for the thermoelastic system in a perforated domain

M. Sango — 2003

Colloquium Mathematicae

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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