Local geometric properties of conductive transmission eigenfunctions and applications

Fuente: arXiv
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Hauptverfasser: Diao, Huaian, Fei, Xiaoxu, Liu, Hongyu
Format: Preprint
Veröffentlicht: 2022
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author Diao, Huaian
Fei, Xiaoxu
Liu, Hongyu
author_facet Diao, Huaian
Fei, Xiaoxu
Liu, Hongyu
contents The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in $\mathbb{R}^n$, $n=2,3$. Second, we apply the spectral property to the geometrical inverse scattering problem of determining the shape as well as its boundary impedance parameter of a conductive scatterer, independent of its medium content, by a single far-field measurement. We establish several new unique recovery results. The results extend the relevant ones in [30] in two directions: first, we consider a more general geometric setup where both polyhedral and conic corners are investigated, whereas in [30] only polyhedral corners are concerned; second, we significantly relax the regularity assumptions in [30] which is particularly useful for the geometrical inverse problem mentioned above. We develop novel technical strategies to achieve these new results.
format Preprint
id arxiv_https___arxiv_org_abs_2206_01933
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Local geometric properties of conductive transmission eigenfunctions and applications
Diao, Huaian
Fei, Xiaoxu
Liu, Hongyu
Analysis of PDEs
The purpose of the paper is twofold. First, we show that partial-data transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in $\mathbb{R}^n$, $n=2,3$. Second, we apply the spectral property to the geometrical inverse scattering problem of determining the shape as well as its boundary impedance parameter of a conductive scatterer, independent of its medium content, by a single far-field measurement. We establish several new unique recovery results. The results extend the relevant ones in [30] in two directions: first, we consider a more general geometric setup where both polyhedral and conic corners are investigated, whereas in [30] only polyhedral corners are concerned; second, we significantly relax the regularity assumptions in [30] which is particularly useful for the geometrical inverse problem mentioned above. We develop novel technical strategies to achieve these new results.
title Local geometric properties of conductive transmission eigenfunctions and applications
topic Analysis of PDEs
url https://arxiv.org/abs/2206.01933