no. 2
Singular Asymptotic Expansions for Dirichlet Eigenvalues and Eigenfunctions of the Laplacian on Thin Planar Domains
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 547-560. 
@article{AIHPC_2009__26_2_547_0,
     author = {Borisov, Denis and Freitas, Pedro},
     title = {Singular {Asymptotic} {Expansions} for {Dirichlet} {Eigenvalues} and {Eigenfunctions} of the {Laplacian} on {Thin} {Planar} {Domains}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {547--560},
     publisher = {Elsevier},
     volume = {26},
     number = {2},
     year = {2009},
     doi = {10.1016/j.anihpc.2007.12.001},
     mrnumber = {2504043},
     zbl = {1168.35401},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2007.12.001/}
}
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Borisov, Denis; Freitas, Pedro. Singular Asymptotic Expansions for Dirichlet Eigenvalues and Eigenfunctions of the Laplacian on Thin Planar Domains. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 547-560. doi : 10.1016/j.anihpc.2007.12.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2007.12.001/

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