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Networks and Heterogeneous Media

2012, Volume 7, Issue 1: 151-178. doi: 10.3934/nhm.2012.7.151
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Steklov problems in perforated domains with a coefficient of indefinite sign

  • 1.
    Department of mathematical sciences, Politecnico, Torino, Corso Duca degli Abruzzi 24, 10129 Torino
  • 2.
    Institute for Problems in Mechanical Engineering RAS, Bolshoi ave., 61, 199178, St-Petersburg
  • 3.
    Narvik University College, Postbox 385, 8505 Narvik
  • Received: 01 September 2011 Revised: 01 January 2012

  • Primary: 35B27.

  • We consider homogenization of Steklov spectral problem for a divergence form elliptic operator in periodically perforated domain under the assumption that the spectral weight function changes sign. We show that the limit behaviour of the spectrum depends essentially on wether the average of the weight function over the boundary of holes is positive, or negative or equal to zero. In all these cases we construct the asymptotics of the eigenpairs.

    Citation: Valeria Chiado Piat, Sergey S. Nazarov, Andrey Piatnitski. Steklov problems in perforated domains with a coefficient of indefinite sign[J]. Networks and Heterogeneous Media, 2012, 7(1): 151-178. doi: 10.3934/nhm.2012.7.151

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  • We consider homogenization of Steklov spectral problem for a divergence form elliptic operator in periodically perforated domain under the assumption that the spectral weight function changes sign. We show that the limit behaviour of the spectrum depends essentially on wether the average of the weight function over the boundary of holes is positive, or negative or equal to zero. In all these cases we construct the asymptotics of the eigenpairs.


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