Revista Matemática Iberoamericana


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Volume 31, Issue 4, 2015, pp. 1423–1458
DOI: 10.4171/RMI/875

Published online: 2015-12-23

A Born approximation from backscattering data for live loads in Lamé system

Juan Antonio Barceló[1], Magali Folch-Gabayet[2], Salvador Pérez-Esteva[3], Alberto Ruiz[4] and Mari Cruz Vilela[5]

(1) Universidad Politécnica de Madrid, Spain
(2) Universidad Nacional Autónoma de México, México, D.F., Mexico
(3) UNAM, Unidad Cuernavaca, Cuernavaca, Mexico
(4) Universidad Autónoma de Madrid, Spain
(5) Universidad de Valladolid, Segovia, Spain

We will study the inverse scattering problem for the Lamé equation in elasticity with live loads. We give the definition of a Born approximation of the load from backscattering data. We will see that in 2D, for non-smooth load matrices the main singularities of the matrices are in fact contained in their Born approximations. The singularities are measured in the scale of Sobolev spaces.

Keywords: Inverse scattering problem, Lamé system, Born approximation

Barceló Juan Antonio, Folch-Gabayet Magali, Pérez-Esteva Salvador, Ruiz Alberto, Cruz Vilela Mari: A Born approximation from backscattering data for live loads in Lamé system. Rev. Mat. Iberoam. 31 (2015), 1423-1458. doi: 10.4171/RMI/875