On the spectrum of a Robin Laplacian in a planar waveguide

Alex Ferreira Rossini

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arXiv · 1606.05291

On the spectrum of a Robin Laplacian in a planar waveguide

Alex Ferreira Rossini

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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 particular types of 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.

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Alex Ferreira Rossini. 2016-06-03. On the spectrum of a Robin Laplacian in a planar waveguide. https://arxiv.org/abs/1606.05291

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