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On the Polarization Matrix for a Perforated Strip

  • Sergey A. Nazarov
  • Rafael Orive-Illera
  • María-Eugenia Pérez-MartínezEmail author
Chapter

Abstract

We consider a boundary value problem for the harmonic functions in an unbounded perforated strip \(\varPi \setminus \overline \omega \), ω being the “Dirichlet hole”, namely a bounded Lipschitz domain of \({\mathbb R}\), 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.

Notes

Acknowledgements

The research of the first author has been partially supported by the Russian Foundation on Basic Research grant 18-01-00325. The research of the second author has been partially supported by MINECO, through the Severo Ochoa Programme for Centres of Excellence in RaD (SEV-2015-0554) and MTM2017-89976-P. The research of the third author has been partially supported by MINECO, MTM2013-44883-P.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sergey A. Nazarov
    • 1
    • 2
  • Rafael Orive-Illera
    • 3
  • María-Eugenia Pérez-Martínez
    • 4
    Email author
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Institute of Problems of Mechanical Engineering RASSt. PetersburgRussia
  3. 3.Universidad Autónoma de MadridMadridSpain
  4. 4.Universidad de CantabriaSantanderSpain

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