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The thick Neumann’s sieve. (English) Zbl 0635.35021
The author considers the thick Neumann’s sieve which is described by the boundary value problem \[ -\Delta u^{\epsilon}+u^{\epsilon}=f\quad in\quad \Omega^{\epsilon};\quad \frac{\partial u^{\epsilon}}{\partial n}=0\quad on\quad \Gamma^{\epsilon};\quad u^{\epsilon}=0\quad on\quad \partial \Omega -\Sigma^{\epsilon} \] where \(\Omega^{\epsilon}=\Omega -\Sigma^{\epsilon}\), \(\Gamma^{\epsilon}={\bar \Omega}\cap \partial \Sigma^{\epsilon}\), \(\Omega\) is an open bounded set of R N, \(\Sigma^{\epsilon}\) is the sieve with thickness \(2h^{\epsilon}\) and the holes of “diameter” \(2r^{\epsilon}\), centred on the hyperplane \(x_ N=0\), \(\epsilon\) is the parameter characterizing the distance between two adjacent holes. He also identifies the limit problem which depends on \(h^{\epsilon}\) and \(r^{\epsilon}\).
Reviewer: F.Jiang

MSC:
35J25 Boundary value problems for second-order elliptic equations
35B20 Perturbations in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
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