Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data

Sonia Foschiatti; Eva Sincich

doi:10.3934/ipi.2022063

Article Contents

2023, Volume 17, Issue 3: 584-613. Doi: 10.3934/ipi.2022063

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Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data

Sonia Foschiatti^1, , and
Eva Sincich^1,

1.
Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Italy

^*Corresponding author: Sonia Foschiatti
^*Corresponding author: Sonia Foschiatti

Received: July 2022

Revised: November 2022

Early access: November 24, 2022

Published online: November 24, 2022

The authors are supported by PRIN grant No. 201758MTR2-007.

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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.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35R25.

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