Approximation of the elastic Dirichlet-to-Neumann map

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2022-01-13 DOI:10.3934/ipi.2022042

G. Vodev

引用次数: 1

Abstract

We study the Dirichlet-to-Neumann map for the stationary linear equation of elasticity in a bounded domain in \begin{document}$ \mathbb{R}^d $\end{document}, \begin{document}$ d\ge 2 $\end{document}, with smooth boundary. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol modulo conjugation by unitary matrices.

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弹性狄利克雷-诺伊曼映射的近似

我们研究了边界光滑的有界域上的平稳线性弹性方程的Dirichlet到Neumann映射。我们证明了它可以用矩阵值符号边界上的伪微分算子来近似，并用酉矩阵计算主符号的模共轭。

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.