A Born approximation from backscattering data for live loads in Lamé system
Juan Antonio Barceló
Universidad Politécnica de Madrid, SpainMagali Folch-Gabayet
Universidad Nacional Autónoma de México, México, D.F., MexicoSalvador Pérez-Esteva
UNAM, Unidad Cuernavaca, Cuernavaca, MexicoAlberto Ruiz
Universidad Autónoma de Madrid, SpainMari Cruz Vilela
Universidad de Valladolid, Segovia, Spain
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Abstract
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.
Cite this article
Juan Antonio Barceló, Magali Folch-Gabayet, Salvador Pérez-Esteva, Alberto Ruiz, Mari Cruz Vilela, A Born approximation from backscattering data for live loads in Lamé system. Rev. Mat. Iberoam. 31 (2015), no. 4, pp. 1423–1458
DOI 10.4171/RMI/875