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 π, and it is void if the domain is concave.

### 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 π, and it is void if the domain is concave.
##### Scheda breve Scheda completa Scheda completa (DC)
2014
55
12
1
19
122101
https://arxiv.org/abs/1406.7624
https://zbmath.org/?t=&s=0&q=Curvature-induced+bound+states+in+Robin+waveguides
Exner, P.; Minakov, Oleksandr
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.11767/32834`
• ND
• 16
• 16