Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-01-11 DOI:10.3934/ipi.2021049

M. Garc'ia-Ferrero, Angkana Ruland, Wiktoria Zato'n

引用次数: 5

Abstract

In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on [3,35]. The results rely on quantitative unique continuation estimates in suitable function spaces with explicit frequency dependence. We contrast the frequency dependence of interior Runge approximation results from non-convex and convex sets.

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声学亥姆霍兹方程部分数据Calderón问题的Runge逼近与稳定性改进

在本文中，我们讨论了声学亥姆霍兹方程的定量Runge近似性质，并证明了基于[3,35]模型的相关部分数据反问题在高频极限下的稳定性改进结果。结果依赖于适当的函数空间中具有显式频率相关性的定量唯一延拓估计。我们比较了非凸集和凸集的内朗格近似结果的频率依赖性。

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.