平面扇形区域中磁性诺伊曼拉普拉斯算子的束缚态
Bound states for the magnetic Neumann Laplacian in planar sectors
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中文总结 AI 辅助
研究平面扇形区域中磁性诺伊曼拉普拉斯算子的束缚态问题，基于前人工作，证明凸扇形区域谱底低于半平面阈值，得出\(H_\alpha\)有离散基态本征值，解决了相关模型问题。
中文摘要 AI 辅助
我们研究了在恒定磁场下开口为\(\alpha\in(0,\pi)\)的无限平面扇形区域中的磁性诺伊曼拉普拉斯算子。基于Bonnaillie-Noël及其合作者以及Exner、Lotoreichik和Pérez-Obiol的早期工作，我们证明了对于每个凸扇形区域，谱底严格低于半平面阈值。因此，对于每个\(0<\alpha<\pi\)，\(H_\alpha\)都有一个离散的基态本征值。这解决了凸扇形区域的束缚态问题，该问题是在角附近的磁定位分析和II型超导电性的第三临界场分析中出现的模型问题。
英文摘要
We study the magnetic Neumann Laplacian in an infinite planar sector of opening $α\in(0,π)$ under a constant magnetic field. Building on earlier work by Bonnaillie-Noël and collaborators and by Exner, Lotoreichik, and Pérez-Obiol, we prove that the bottom of the spectrum lies strictly below the half-plane threshold for every convex sector. Consequently, $H_α$ has a discrete ground-state eigenvalue for every $0<α<π$. This resolves the bound-state problem for convex sectors, a model problem arising in the analysis of magnetic localization near corners and of the third critical field in type-II superconductivity.
