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

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dc.creatorStefanov, Plamen
dc.creatorUhlmann, Gunther
dc.date2008-09-01
dc.date.accessioned2026-07-07T09:59:46Z
dc.date.available2026-07-07T09:59:46Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/0809.0270
dc.identifierhttp://arxiv.org/abs/0809.0270
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168141
dc.subjectFunctional Analysis
dc.subjectAnalysis of PDEs
dc.subject35R30
dc.titleLinearizing non-linear inverse problems and an application to inverse backscattering
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