On the spectrum of Robin Laplacian in a planar waveguide
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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.
Keywordsplanar waveguide discrete spectrum Robin boundary conditions
MSC47B25 47F05 49R05 81Q10
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