Titlebook: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II; Volume II Vladimir Maz’ya,Serguei Nazarov,

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On the ,-Calculus Augmented with SabotageHomogenization can be useful not only for studying differential equations but for difference ones, as well. Moreover, to difference equations it was applied even earlier, in the nineteenth century, to analyze the limit passages in discrete models of continua for obtaining continuous ones.

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The Dirichlet Problem in Domains with Thin LigamentsWe consider the Dirichlet problem for the Laplace equation in a domain .. depending on a small parameter ε. It is supposed that a part of the domain is located between two close surfaces which are separated by a distance .(ε). The purpose is to study the asymptotic behavior of solutions as ε → 0.

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Homogenization of Equations on a Fine Periodic GridHomogenization can be useful not only for studying differential equations but for difference ones, as well. Moreover, to difference equations it was applied even earlier, in the nineteenth century, to analyze the limit passages in discrete models of continua for obtaining continuous ones.

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Théo Pierron,Thomas Place,Marc Zeitounclosed curve or a segment. In Section 12.1 and 12.2 we consider the Neumann and Dirichlet problems for the Laplace operator in the exterior of a thin closed tube. The first boundary value problem for the Lamé system in the same geometric situation is studied in Section 12.3. Then we return to the La