共形横向各向异性流形上非线性磁性Schrödinger方程的反问题

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-16 DOI:10.2140/apde.2023.16.1825

Katya Krupchyk, Gunther Uhlmann

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引用次数: 17

摘要

研究了维数为$n\ \ 3$的共形横向各向异性黎曼流形上的非线性磁性薛定谔算子的反边界问题。在适当的非线性假设下，我们证明了流形边界上的Dirichlet-to-Neumann映射的知识唯一地决定了非线性磁势和电势。在这个结果中没有对横向流形作任何假设，而线性磁性薛定谔算子的相应逆边界问题在这个一般情况下仍然是开放的。

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Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds

We study the inverse boundary problem for a nonlinear magnetic Schrodinger operator on a conformally transversally anisotropic Riemannian manifold of dimension $n\ge 3$. Under suitable assumptions on the nonlinearity, we show that the knowledge of the Dirichlet-to-Neumann map on the boundary of the manifold determines the nonlinear magnetic and electric potentials uniquely. No assumptions on the transversal manifold are made in this result, whereas the corresponding inverse boundary problem for the linear magnetic Schrodinger operator is still open in this generality.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.