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On the spectrum of Robin Laplacian in a planar waveguide

  • Alex Ferreira Rossini
Article
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Abstract

We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian when the boundary coupling function has a limit at infinity. Furthermore, we derive sufficient conditions for the existence of discrete spectrum.

Keywords

planar waveguide discrete spectrum Robin boundary conditions 

MSC

47B25 47F05 49R05 81Q10 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Instituto de MatemáticaUniversidade Federal de Mato Grosso do Sul, Cidade UniversitáriaCampo GrandeBrazil

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