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Applicable Analysis
An International Journal
Volume 61, 1996 - Issue 3-4
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Original Articles

On the Eigenvalues of the Laplace Operator on a Thin Set with Neumann Boundary Conditions

Michelle Schatzman
Pages 293-306 | Published online: 02 May 2007

Citations (22)

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Read on this site (3)

Toshiaki Yachimura. (2019) Asymptotic behavior for the principal eigenvalue of a reinforcement problem. Applicable Analysis 98:10, pages 1946-1958.
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Peter Kuchment. (2002) Graph models for waves in thin structures. Waves in Random Media 12:4, pages R1-R24.
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Peter Kuchment & LeonidA. Kunyansky. (1999) Spectral Properties of High Contrast Band-Gap Materials and Operators on Graphs. Experimental Mathematics 8:1, pages 1-28.
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Articles from other publishers (19)

Francesco Ferraresso & Luigi Provenzano. (2023) On the eigenvalues of the biharmonic operator with Neumann boundary conditions on a thin set. Bulletin of the London Mathematical Society 55:3, pages 1154-1177.
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Francesco Ferraresso. (2022) On the spectral instability for weak intermediate triharmonic problems. Mathematical Methods in the Applied Sciences 45:10, pages 5864-5891.
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Tatsu-Hiko Miura. (2020) Navier–Stokes Equations in a Curved Thin Domain, Part II: Global Existence of a Strong Solution. Journal of Mathematical Fluid Mechanics 23:1.
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David Krejčiřík & Matěj Tušek. (2019) Location of hot spots in thin curved strips. Journal of Differential Equations 266:6, pages 2953-2977.
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César R. de Oliveira, Luiz Hartmann & Alessandra A. Verri. (2019) Effective Hamiltonians in surfaces of thin quantum waveguides. Journal of Mathematical Physics 60:2.
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Carlos R. Mamani & Alessandra A. Verri. (2018) Influence of bounded states in the Neumann Laplacian in a thin waveguide. Rocky Mountain Journal of Mathematics 48:6.
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Bjørn Jensen, Rossen Dandoloff & Avadh Saxena. (2014) Quantum particle constrained to a surface in quantum hydrodynamics. Physica Scripta 89:10, pages 105202.
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D. S. Grebenkov & B.-T. Nguyen. (2013) Geometrical Structure of Laplacian Eigenfunctions. SIAM Review 55:4, pages 601-667.
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DAVID KREJČIŘÍK & HELENA ŠEDIVÁKOVÁ. (2012) THE EFFECTIVE HAMILTONIAN IN CURVED QUANTUM WAVEGUIDES UNDER MILD REGULARITY ASSUMPTIONS. Reviews in Mathematical Physics 24:07, pages 1250018.
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David Krejčiřík. (2008) Spectrum of the Laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations 15:3, pages 555-568.
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B. Pavlov. 2010. Characteristic Functions, Scattering Functions and Transfer Functions. Characteristic Functions, Scattering Functions and Transfer Functions 281 336 .
B. S. Pavlov. (2008) Krein formula with compensated singularities for the ND-mapping and the generalized Kirchhoff condition at the Neumann Schrödinger junction. Russian Journal of Mathematical Physics 15:3, pages 364-388.
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N. T. Bagraev, A. B. Mikhailova, B. S. Pavlov, L. V. Prokhorov & A. M. Yafyasov. (2005) Parameter regime of a resonance quantum switch. Physical Review B 71:16.
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Peter Kuchment. 2003. Analysis and Applications — ISAAC 2001. Analysis and Applications — ISAAC 2001 7 30 .
Eduard Marušić-Paloka. 2003. Applied Mathematics and Scientific Computing. Applied Mathematics and Scientific Computing 237 249 .
Eduard Marušić-Paloka. (2001) Average of the Navier's Law on the Rapidly Oscillating Boundary. Journal of Mathematical Analysis and Applications 259:2, pages 685-701.
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Peter Kuchment & Hongbiao Zeng. (2001) Convergence of Spectra of Mesoscopic Systems Collapsing onto a Graph. Journal of Mathematical Analysis and Applications 258:2, pages 671-700.
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W. Axmann, P. Kuchment & L. Kunyansky. (1999) Asymptotic methods for thin high-contrast two-dimensional PBG materials. Journal of Lightwave Technology 17:11, pages 1996-2007.
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Jacob Rubinstein & Michelle Schatzman. (1997) Spectral and variational problems on multiconnected strips. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 325:4, pages 377-382.
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