共形横向各向异性流形上磁薛定谔算子的部分数据逆问题

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Asymptotic Analysis Pub Date : 2024-04-29 DOI:10.3233/asy-241909

Salem Selim, Lili Yan

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引用次数: 0

摘要

我们研究了在维数为 n⩾3 且边界相连的保角横向各向异性黎曼流形上具有荷尔德连续磁势和连续电势的磁薛定谔算子的逆边界问题。只要横向流形上的大地 X 射线变换是注入式的，就能根据流形边界上的部分考奇数据建立磁场和电势的全局唯一性结果。

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Partial data inverse problems for magnetic Schrödinger operators on conformally transversally anisotropic manifolds

We study inverse boundary problems for the magnetic Schrödinger operator with Hölder continuous magnetic potentials and continuous electric potentials on a conformally transversally anisotropic Riemannian manifold of dimension n⩾3 with connected boundary. A global uniqueness result is established for magnetic fields and electric potentials from the partial Cauchy data on the boundary of the manifold provided that the geodesic X-ray transform on the transversal manifold is injective.

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来源期刊

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.