International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 651390, 12 pages
http://dx.doi.org/10.1155/2012/651390
Research Article

Inverse Problem for a Curved Quantum Guide

Laure Cardoulis1,2 and Michel Cristofol3

1UT1 Ceremath, Université de Toulouse, 21 Allées de Brienne, 31042 Toulouse Cedex 9, France
2Institut de Mathématiques de Toulouse, Université Paul Sabatier, UMR 5219, 31062 Toulouse Cedex 9, France
3LATP, Université d'Aix-Marseille, UMR 7353, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France

Received 28 March 2012; Accepted 22 June 2012

Academic Editor: Wolfgang Castell

Copyright © 2012 Laure Cardoulis and Michel Cristofol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the Dirichlet Laplacian operator − Δ on a curved quantum guide in ℝ 𝑛 ( 𝑛 = 2 , 3 ) with an asymptotically straight reference curve. We give uniqueness results for the inverse problem associated to the reconstruction of the curvature by using either observations of spectral data or a boot-strapping method.