On the Polarization Matrix for a Perforated Strip

Sergey A. Nazarov, Rafael Orive-Illera () and María-Eugenia Pérez-Martínez ()
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Sergey A. Nazarov: St. Petersburg State University
Rafael Orive-Illera: Universidad Autónoma de Madrid
María-Eugenia Pérez-Martínez: Universidad de Cantabria

Chapter Chapter 21 in Integral Methods in Science and Engineering, 2019, pp 267-281 from Springer

Abstract: Abstract We consider a boundary value problem for the harmonic functions in an unbounded perforated strip Π ∖ ω ¯ $$\varPi \setminus \overline \omega $$ , ω being the “Dirichlet hole”, namely a bounded Lipschitz domain of ℝ $${\mathbb R}$$ , where a Dirichlet condition is prescribed. The other boundary conditions are periodicity conditions on the lateral boundary of Π = (0, H) × (−∞, ∞). We study properties of the coefficients of the so-called polarization matrix, while we highlight the dependence of these coefficients on the dimensions of the hole by means of two examples.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-16077-7_21

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DOI: 10.1007/978-3-030-16077-7_21

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