Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913460083752960 |
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| author | Foschiatti, Sonia Sincich, Eva |
| author_facet | Foschiatti, Sonia Sincich, Eva |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_07598 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data Foschiatti, Sonia Sincich, Eva Analysis of PDEs Mathematical Physics 35R30 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. |
| title | Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data |
| topic | Analysis of PDEs Mathematical Physics 35R30 |
| url | https://arxiv.org/abs/2207.07598 |