Geodesic
Asymptotics of eigenvalues of the Dirichlet problem in a skewed $\mathcal{T}$-shaped waveguide
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 793-814

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Asymptotics are constructed and justified for the eigenvalues of the Dirichlet problem for the Laplacian in a waveguide consisting of a unit strip and a semi-infinite strip joined at a small angle $\varepsilon\in(0,\pi/2)$. Some properties of the discrete spectrum are established, and open questions are stated. 
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     author = {S. A. Nazarov},
     title = {Asymptotics of eigenvalues of the {Dirichlet} problem in a skewed $\mathcal{T}$-shaped waveguide},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {793--814},
     publisher = {mathdoc},
     volume = {54},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_5_a7/}
}
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S. A. Nazarov. Asymptotics of eigenvalues of the Dirichlet problem in a skewed $\mathcal{T}$-shaped waveguide. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 793-814. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_5_a7/