Linearizing non-linear inverse problems and an application to inverse backscattering

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We propose an abstract approach to prove local uniqueness and conditional Hölder stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization $A$, we need a stability estimate for $A$ as well. That condition is satisfied in particular, if $A^*A$ is an elliptic pseudo-differential operator. We apply this scheme to show uniqueness and Hölder stability for the inverse backscattering problem for the acoustic equation near a constant sound speed.

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Functional Analysis, Analysis of PDEs, 35R30

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http://salesiana.dossiersoluciones.com/handle/123456789/168141

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0809.0270
 http://arxiv.org/abs/0809.0270

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arXiv