We consider the inverse problem of determining an inclusion contained in a body for a Schrödinger type equation by means of local Cauchy data. Both the body and the inclusion are made by inhomogeneous and anisotropic materials. Under mild a priori assumptions on the unknown inclusion, we establish a logarithmic stability estimate in terms of the local Cauchy data. In view of possible applications, we also provide a stability estimate in terms of an ad-hoc misfit functional.
Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data
Sonia Foschiatti
;eva sincich
2023-01-01
Abstract
We consider the inverse problem of determining an inclusion contained in a body for a Schrödinger type equation by means of local Cauchy data. Both the body and the inclusion are made by inhomogeneous and anisotropic materials. Under mild a priori assumptions on the unknown inclusion, we establish a logarithmic stability estimate in terms of the local Cauchy data. In view of possible applications, we also provide a stability estimate in terms of an ad-hoc misfit functional.File in questo prodotto:
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