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://www.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://www.numdam.org/articles/10.1016/j.anihpc.2007.12.001/

[1] Antunes P., Freitas P., A Numerical Study of the Spectral Gap, J. Phys. A 41 (2008). | MR | Zbl

[2] Berezin F. A., Shubin M. A., The Schrödinger Equation, Kluwer, Dordrecht, 1991. | MR | Zbl

[3] Freitas P., Precise Bounds and Asymptotics for the First Dirichlet Eigenvalue of Triangles and Rhombi, J. Funct. Anal. 251 (2007) 376-398. | MR | Zbl

[4] P. Freitas, D. Krejčiřík, A sharp upper bound for the first Dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains, Proc. Amer. Math. Soc., in press. | MR | Zbl

[5] L. Friedlander, M. Solomyak, On the spectrum of the Dirichlet Laplacian in a narrow strip, preprint, 2007. | MR | Zbl

[6] Joseph D. D., Parameter and Domain Dependence of Eigenvalues of Elliptic Partial Differential Equations, Arch. Ration. Mech. Anal. 24 (1967) 325-351. | MR | Zbl

[7] Ladyzhenskaya O. A., Uraltseva N. N., Linear and Quasilinear Elliptic Equations, Academic Press, New York-London, 1968. | MR | Zbl

[8] Olejnik O. A., Shamaev A. S., Yosifyan G. A., Mathematical Problems in Elasticity and Homogenization, Studies in Mathematics and its Applications, vol. 26, North-Holland, Amsterdam, 1992. | MR | Zbl

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