Volume 15, Number 3, July-September 2009
|Page(s)||555 - 568|
|Published online||30 May 2008|
- 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.
- 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. Carron, P. Exner and D. Krejčiřík, Topologically nontrivial quantum layers. J. Math. Phys. 45 (2004) 774–784. [CrossRef] [MathSciNet]
- E.B. Davies, Spectral theory and differential operators. Camb. Univ. Press, Cambridge (1995).
- J. Dittrich and J. Kříž, Curved planar quantum wires with Dirichlet and Neumann boundary conditions. J. Phys. A 35 (2002) L269–L275. [CrossRef]
- 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. Duclos, P. Exner and D. Krejčiřík, Bound states in curved quantum layers. Commun. Math. Phys. 223 (2001) 13–28. [CrossRef]
- P. Exner and P. Šeba, Bound states in curved quantum waveguides. J. Math. Phys. 30 (1989) 2574–2580. [CrossRef] [MathSciNet]
- P. Freitas, Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi. J. Funct. Anal. 251 (2007) 376–398. [CrossRef] [MathSciNet]
- P. Freitas and D. Krejčiřík, Instability results for the damped wave equation in unbounded domains. J. Diff. Eq. 211 (2005) 168–186. [CrossRef]
- P. Freitas and D. Krejčiřík, Waveguides with combined Dirichlet and Robin boundary conditions. Math. Phys. Anal. Geom. 9 (2006) 335–352. [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 strip, I. Israel J. Math. (to appear).
- L. Friedlander and M. Solomyak, On the spectrum of the Dirichlet Laplacian in a narrow strip, II. Amer. Math. Soc. (to appear).
- J. Goldstone and R.L. Jaffe, Bound states in twisting tubes. Phys. Rev. B 45 (1992) 14100–14107. [CrossRef]
- 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).
- 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]
- 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.
- D. Krejčiřík, Quantum strips on surfaces. J. Geom. Phys. 45 (2003) 203–217. [CrossRef] [MathSciNet]
- D. Krejčiřík, Hardy inequalities in strips on ruled surfaces. J. Inequal. Appl. 2006 (2006) 46409.
- D. Krejčiřík and J. Kříž, On the spectrum of curved quantum waveguides. Publ. RIMS, Kyoto University 41 (2005) 757–791.
- Ch. Lin and Z. Lu, Existence of bound states for layers built over hypersurfaces in . J. Funct. Anal. 244 (2007) 1–25. [CrossRef] [MathSciNet]
- Ch. Lin and Z. Lu, Quantum layers over surfaces ruled outside a compact set. J. Math. Phys. 48 (2007) 053522. [CrossRef] [MathSciNet]
- 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]
- M. Reed and B. Simon, Methods of modern mathematical physics, I. Functional analysis. Academic Press, New York (1972).
- 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]
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