发表机构
University of Ostrava; VSB – Technical University of Ostrava; Charles University, Prague（俄斯特拉发大学; 俄斯特拉发理工大学; 布拉格查理大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究曲线半平面上带紧支磁场的磁Robin拉普拉斯算子，证明其谱在边界小局部变形下稳定，解决了Robin拉普拉斯谱对边界变形不稳定的问题。
AI 中文摘要
我们分析具有光滑边界的曲线半平面上的磁Robin拉普拉斯算子。已知Robin拉普拉斯算子的谱对边界变形不稳定：当边界为直线时，其谱完全是本质谱；而边界的扰动会在本质谱下方产生本征值。本文考虑具有紧支磁场的Robin-Laplace算子，证明磁Robin拉普拉斯算子的谱在边界的小且局部的变形下是稳定的。
英文摘要
We analyse magnetic Robin Laplacian in curvilinear half-plane with a smooth boundary. It is well known that the spectrum of the Robin Laplacian is unstable with respect to boundary deformations. This means that if the boundary is a straight line then the spectrum of the Robin Laplacian is purely essential. From the other hand, the perturbation of the boundary produces eigenvalues below the essential spectrum. In this paper, the Robin-Laplace operator with a compactly supported magnetic field is considered. We prove that the spectrum of the magnetic Robin Laplacian is stable under small and local deformations of the boundary.
