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All issues Volume 15 / No 3 (July-September 2009) ESAIM: COCV, 15 3 (2009) 555-568 References
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Issue
ESAIM: COCV
Volume 15, Number 3, July-September 2009
Page(s) 555 - 568
DOI https://doi.org/10.1051/cocv:2008035
Published online 30 May 2008
  1. D. Borisov and P. Freitas, Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin planar domains. Ann. Inst. H. Poincaré Anal. Non Linéaire (2008) doi: 10.1016/j.anihpc.2007.12.001. [Google Scholar]
  2. 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]
  3. G. Carron, P. Exner and D. Krejčiřík, Topologically nontrivial quantum layers. J. Math. Phys. 45 (2004) 774–784. [CrossRef] [MathSciNet] [Google Scholar]
  4. E.B. Davies, Spectral theory and differential operators. Camb. Univ. Press, Cambridge (1995). [Google Scholar]
  5. J. Dittrich and J. Kříž, Curved planar quantum wires with Dirichlet and Neumann boundary conditions. J. Phys. A 35 (2002) L269–L275. [Google Scholar]
  6. 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]
  7. P. Duclos, P. Exner and D. Krejčiřík, Bound states in curved quantum layers. Commun. Math. Phys. 223 (2001) 13–28. [CrossRef] [Google Scholar]
  8. P. Exner and P. Šeba, Bound states in curved quantum waveguides. J. Math. Phys. 30 (1989) 2574–2580. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Freitas, Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi. J. Funct. Anal. 251 (2007) 376–398. [CrossRef] [MathSciNet] [Google Scholar]
  10. P. Freitas and D. Krejčiřík, Instability results for the damped wave equation in unbounded domains. J. Diff. Eq. 211 (2005) 168–186. [CrossRef] [Google Scholar]
  11. P. Freitas and D. Krejčiřík, Waveguides with combined Dirichlet and Robin boundary conditions. Math. Phys. Anal. Geom. 9 (2006) 335–352. [CrossRef] [MathSciNet] [Google Scholar]
  12. 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]
  13. L. Friedlander and M. Solomyak, On the spectrum of the Dirichlet Laplacian in a narrow strip, I. Israel J. Math. (to appear). [Google Scholar]
  14. L. Friedlander and M. Solomyak, On the spectrum of the Dirichlet Laplacian in a narrow strip, II. Amer. Math. Soc. (to appear). [Google Scholar]
  15. J. Goldstone and R.L. Jaffe, Bound states in twisting tubes. Phys. Rev. B 45 (1992) 14100–14107. [CrossRef] [Google Scholar]
  16. D. Grieser, Thin tubes in mathematical physics, global analysis and spectral geometry, in Analysis on Graphs and its Applications (Cambridge, 2007), Proceedings of Symposia in Pure Mathematics, Amer. Math. Soc. (to appear). [Google Scholar]
  17. E.R. Johnson, M. Levitin and L. Parnovski, Existence of eigenvalues of a linear operator pencil in a curved waveguide – localized shelf waves on a curved coast. SIAM J. Math. Anal. 37 (2006) 1465–1481. [CrossRef] [MathSciNet] [Google Scholar]
  18. L. Karp and M. Pinsky, First-order asymptotics of the principal eigenvalue of tubular neighborhoods, in Geometry of random motion (Ithaca, N.Y., 1987), Contemp. Math. 73, Amer. Math. Soc., Providence, RI (1988) 105–119. [Google Scholar]
  19. D. Krejčiřík, Quantum strips on surfaces. J. Geom. Phys. 45 (2003) 203–217. [CrossRef] [MathSciNet] [Google Scholar]
  20. D. Krejčiřík, Hardy inequalities in strips on ruled surfaces. J. Inequal. Appl. 2006 (2006) 46409. [Google Scholar]
  21. D. Krejčiřík and J. Kříž, On the spectrum of curved quantum waveguides. Publ. RIMS, Kyoto University 41 (2005) 757–791. [Google Scholar]
  22. Ch. Lin and Z. Lu, Existence of bound states for layers built over hypersurfaces in Formula . J. Funct. Anal. 244 (2007) 1–25. [CrossRef] [MathSciNet] [Google Scholar]
  23. Ch. Lin and Z. Lu, Quantum layers over surfaces ruled outside a compact set. J. Math. Phys. 48 (2007) 053522. [CrossRef] [MathSciNet] [Google Scholar]
  24. O. Olendski and L. Mikhailovska, Localized-mode evolution in a curved planar waveguide with combined Dirichlet and Neumann boundary conditions. Phys. Rev. E 67 (2003) 056625. [CrossRef] [MathSciNet] [Google Scholar]
  25. M. Reed and B. Simon, Methods of modern mathematical physics, I. Functional analysis. Academic Press, New York (1972). [Google Scholar]
  26. M. Schatzman, On the eigenvalues of the Laplace operator on a thin set with Neumann boundary conditions. Appl. Anal. 61 (1996) 293–306. [CrossRef] [MathSciNet] [Google Scholar]

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