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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-07-15 DOI:10.3934/ipi.2022063

Sonia Foschiatti, E. Sincich

引用次数: 2

Abstract

We consider the inverse problem of determining an inclusion contained in a body for a Schr\"odinger 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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从局部Cauchy数据稳定地确定Schrödinger方程中的各向异性包含

我们考虑了确定Schr方程体中包含的包含项的反问题\“利用局部柯西数据建立的奥丁格型方程。物体和包裹体都是由非均匀和各向异性材料制成的。在对未知包裹体的温和先验假设下，我们根据局部柯西数据建立了对数稳定性估计。鉴于可能的应用，我们还提供了一个特殊失配函数的稳定性估计。”。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.