Example of a periodic Neumann waveguide with a gap in its spectrum

  • Giuseppe Cardone

    Università del Sannio, Benevento, Italy
  • Andrii Khrabustovskyi

    Karlsruher Institut für Technologie, Germany
Example of a periodic Neumann waveguide with a gap in its spectrum cover
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Abstract

In this note we investigate spectral properties of a periodic waveguide ( is a small parameter) obtained from a straight strip by attaching an array of -periodically distributed identical protuberances having "room-and-passage" geometry. In the current work we consider the operator , where is the Neumann Laplacian in , the weight is equal to everywhere except the union of the „rooms". We will prove that the spectrum of has at least one gap as is small enough provided certain conditions on the weight and the sizes of attached protuberances hold.