Waveguides with Combined Dirichlet and Robin Boundary Conditions
نویسندگان
چکیده
منابع مشابه
Waveguides with combined Dirichlet and Robin boundary conditions
We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a D...
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We discuss the limit of small width for the Laplacian defined on a waveguide with Robin boundary conditions. Under suitable hypothesis on the scaling of the curvature, we prove the convergence of the Robin Laplacian to the Laplacian on the corresponding graph. We show that the projections on each transverse mode generically give rise to decoupling conditions between the edges of the graph while...
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For p ∈ (1,+∞) and b ∈ (0,+∞] the p-torsion function with Robin boundary conditions associated to an arbitrary open set Ω ⊂ R satisfies formally the equation −∆p = 1 in Ω and |∇u|p−2 ∂u ∂n + b|u| p−2u = 0 on ∂Ω. We obtain bounds of the L∞ norm of u only in terms of the bottom of the spectrum (of the Robin p-Laplacian), b and the dimension of the space in the following two extremal cases: the li...
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Quantum waveguides with Dirichlet boundary conditions were extensively studied (e.g. [1], [2], [3], [4], [5], [6] and references therein). Their spectral properties essentially depends on the geometry of the waveguide, especially the existence of bound states induced by curvature [1], [2], [3] or by coupling of straight waveguides through windows [4],[5] were shown. The waveguides with Neumann ...
متن کاملStraight Quantum Waveguide with Robin Boundary Conditions⋆
Abstract. We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we localize the essential spectrum and derive a sufficient condition which guarantees the existence of bound states. Further properties of the associated...
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ژورنال
عنوان ژورنال: Mathematical Physics, Analysis and Geometry
سال: 2007
ISSN: 1385-0172,1572-9656
DOI: 10.1007/s11040-007-9015-6