- N.S. Bakhvalov and G.P. Panasenko, Homogenization: Averaging processes in periodic media. Kluwer, Dordrecht/Boston/ London (1989).
- D. Borisov and P. Freitas, Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions on thin planar domains. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 547–560.
- G. Bouchitté, M.L. Mascarenhas and L. Trabucho, On the curvature and torsion effects in one dimensional waveguides. ESAIM: COCV 13 (2007) 793–808. [CrossRef] [EDP Sciences]
- G. Cardone, T. Durante and S.A. Nazarov, The localization effect for eigenfunctions of the mixed boundary value problem in a thin cylinder with distorted ends. SIAM J. Math. Anal. (to appear).
- P. Duclos and P. Exner, Curvature-induced bound states in quantum waveguides in two and three dimensions. Rev. Math. Phys. 7 (1995) 73–102. [CrossRef] [MathSciNet]
- P. Freitas and D. Krejčiřík, Location of the nodal set for thin curved tubes. Indiana Univ. Math. J. 57 (2008) 343–376. [CrossRef] [MathSciNet]
- L. Friedlander and M. Solomyak, On the spectrum of the Dirichlet Laplacian in a narrow infinite strip, in Spectral theory of differential operators: M. Sh. Birman 80th anniversary collection, Adv. Math. Sci. 225, T. Suslina and D. Yafaev Eds., AMS Translations – Series 2, Providence (2008).
- L. Friedlander and M. Solomyak, On the spectrum of the Dirichlet Laplacian in a narrow strip. Israel J. Math. 170 (2009) 337–354. [CrossRef] [MathSciNet]
- D. Grieser, Thin tubes in mathematical physics, global analysis and spectral geometry, in Analysis on Graphs and Its Applications, P. Exner, J.P. Keating, P. Kuchment, T. Sunada and A. Teplyaev Eds., Proc. Symp. Pure Math. 77, AMS, Providence (2008).
- D. Krejčiřík, Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions. ESAIM: COCV 15 (2009) 555–568. [CrossRef] [EDP Sciences]
- V.P. Mikhajlov, Partial differential equations. Moscow, Mir Publishers (1978).
- S.A. Nazarov, Dimension Reduction and Integral Estimates, Asymptotic Theory of Thin Plates and Rods 1. Novosibirsk, Nauchnaya Kniga (2001).
- O.A. Oleinik, A.S. Shamaev and G.A. Yosifyan, Mathematical problems in elasticity and homogenization, Studies in Mathematics and its Applications 26. Amsterdam etc., North-Holland (1992).
- G.P. Panasenko and M.E. Perez, Asymptotic partial decomposition of domain for spectral problems in rod structures. J. Math. Pures Appl. 87 (2007) 1–36. [CrossRef] [MathSciNet]
- M.I. Vishik and L.A. Lyusternik, The asymptotic behaviour of solutions of linear differential equations with large or quickly changing coefficients and boundary conditions. Russ. Math. Surv. 15 (1960) 23–91. [CrossRef]
Volume 17, Number 3, July-September 2011
|Page(s)||887 - 908|
|Published online||06 August 2010|