Curvature-induced bound states in Robin waveguides and their asymptotical properties

Abstract

We analyze bound states of Robin Laplacian in infinite planar domains with a smooth boundary, in particular, their relations to the geometry of the latter. The domains considered have locally straight boundary being, for instance, locally deformed halfplanes or wedges, or infinite strips, alternatively they are the exterior of a bounded obstacle. In the situation when the Robin condition is strongly attractive, we derive a two-term asymptotic formula in which the next-to-leading term is determined by the extremum of the boundary curvature. We also discuss the non-asymptotic case of attractive boundary interaction and show that the discrete spectrum is nonempty if the domain is a local deformation of a halfplane or a wedge of angle less than $\pi$, and it is void if the domain is concave.

References in corpus (4)

• Asymptotic eigenvalue estimates for a Robin problem with a large parameter
• Waveguides with combined Dirichlet and Robin boundary conditions
• Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration
• Straight Quantum Waveguide with Robin Boundary Conditions

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