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.
2023
nov-2022
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https://www.aimsciences.org//article/doi/10.3934/ipi.2022063
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3027125
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