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

Juan Antonio Barceló | Zendy; Magali Folch-Gabayet | Zendy; Salvador PérezEsteva | Zendy; Alberto Ruiz | Zendy; M. C. Vilela | Zendy

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

Author(s) -

Juan Antonio Barceló,

Magali Folch-Gabayet,

Salvador PérezEsteva,

Alberto Ruiz,

M. C. Vilela

Publication year - 2015

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/875

Subject(s) - gravitational singularity , sobolev space , elasticity (physics) , mathematics , born approximation , mathematical analysis , scattering , inverse , scale (ratio) , physics , geometry , optics , quantum mechanics , thermodynamics

We will study the inverse scattering problem for the Lame 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.

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