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Lipschitz stability for an elliptic inverse problem with two measurements

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arxiv 2404.13901 v5 pith:W43FPGCV submitted 2024-04-22 math.AP

Mourad Choulli , Hiroshi Takase This is my paper · ORCID
classification math.AP
keywords problemboundarylipschitzboundedellipticinversesolutionstability
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abstract

We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain surrounding $B$. We obtain for this inverse problem Lipschitz stability for an admissible class of unknown boundary functions. Our analysis applies as well to an interior problem. We also give an extension to the parabolic case.

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  1. An inverse obstacle problem for the magnetic Schr\"odinger equation

    math.AP 2024-11 conditional novelty 6.0 of 10

    A new Carleman inequality yields Lipschitz (local) and logarithmic (global) stability estimates for an inverse obstacle problem for the magnetic Schrödinger equation.

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