Geodesic
On the spectrum of Robin Laplacian in a planar waveguide
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 485-501 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/CMJ.2018.0396-17
Classification : 47B25, 47F05, 49R05, 81Q10
Keywords: planar waveguide; discrete spectrum; Robin boundary conditions 
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Rossini, Alex Ferreira. On the spectrum of Robin Laplacian in a planar waveguide. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 485-501. doi: 10.21136/CMJ.2018.0396-17

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