Free Access
Issue |
ESAIM: COCV
Volume 17, Number 3, July-September 2011
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Page(s) | 887 - 908 | |
DOI | https://doi.org/10.1051/cocv/2010028 | |
Published online | 06 August 2010 |
- N.S. Bakhvalov and G.P. Panasenko, Homogenization: Averaging processes in periodic media. Kluwer, Dordrecht/Boston/ London (1989). [Google Scholar]
- 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. [Google Scholar]
- 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] [Google Scholar]
- 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). [Google Scholar]
- 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] [Google Scholar]
- P. Freitas and D. Krejčiřík, Location of the nodal set for thin curved tubes. Indiana Univ. Math. J. 57 (2008) 343–376. [CrossRef] [MathSciNet] [Google Scholar]
- 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). [Google Scholar]
- 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] [Google Scholar]
- 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). [Google Scholar]
- 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] [Google Scholar]
- V.P. Mikhajlov, Partial differential equations. Moscow, Mir Publishers (1978). [Google Scholar]
- S.A. Nazarov, Dimension Reduction and Integral Estimates, Asymptotic Theory of Thin Plates and Rods 1. Novosibirsk, Nauchnaya Kniga (2001). [Google Scholar]
- 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). [Google Scholar]
- 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] [Google Scholar]
- 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] [Google Scholar]
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