On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes
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Publication:541272
DOI10.1016/j.jmaa.2011.03.022zbMath1220.35101arXiv1103.2934OpenAlexW2030575249MaRDI QIDQ541272
César R. de Oliveira, Alessandra A. Verri
Publication date: 6 June 2011
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1103.2934
Asymptotic behavior of solutions to PDEs (35B40) General topics in linear spectral theory for PDEs (35P05) Spectrum, resolvent (47A10)
Related Items (12)
THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS ⋮ Generalised quantum waveguides ⋮ Norm resolvent approximation of thin homogeneous tubes by heterogeneous ones ⋮ Effective Hamiltonians in surfaces of thin quantum waveguides ⋮ Absolute continuity and band gaps of the spectrum of the Dirichlet Laplacian in periodic waveguides ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ CONVERGENCE OF SOLUTIONS TO SOME ELLIPTIC EQUATIONS IN BOUNDED NEUMANN THIN DOMAINS ⋮ On the spectrum of Robin Laplacian in a planar waveguide ⋮ On Norm Resolvent and Quadratic Form Convergences in Asymptotic Thin Spatial Waveguides ⋮ Planar waveguide with “twisted” boundary conditions: Small width ⋮ Norm resolvent convergence of Dirichlet Laplacian in unbounded thin waveguides ⋮ Thin waveguides with Robin boundary conditions
Cites Work
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- Geometrically induced discrete spectrum in curved tubes
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- Coupling in the singular limit of thin quantum waveguides
- Twisting versus bending in quantum waveguides
- Resonances in twisted quantum waveguides
- Eigenvalue Asymptotics in a Twisted Waveguide
- Bound states in tubular quantum waveguides with torsion
- CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
- Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions
- On the curvature and torsion effects in one dimensional waveguides
- Location of the nodal set for thin curved tubes
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