Abstract
The paper considers the singularly perturbed Dirichlet problem −ɛΔu ɛ+u ɛ=f in a randomly perforated domain Ωɛ, which is obtained from a bounded open set Ω in R N after removing many holes of size ɛ q . The perforated domain is described in terms of an ergodic dynamical system acting on a probability space. Imposing certain conditions on the domain, the behaviour of u ɛ when ɛ→ 0 in Lebesgue spaces L n (Ω) is studied. Test functions together with the Birkhoff ergodic theorem are the main tools of analysis. The Poisson distribution of holes of size ɛ p with the intensity λɛ− r is then considered. The above results apply in some cases; other cases are treated by the Wiener sausage approach.
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