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

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging 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

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.