论文标题
3D磁力laplacian的非单调性
Non-monotonicity for the 3D magnetic Robin Laplacian
论文作者
论文摘要
以前的作品为二维情况下的磁拉曲板的最低特征值提供了几个反例。但是，三维情况的研究较少。我们使用Helffer，Kachmar和Raymond获得的结果，在3D中提供了最早的反例之一。考虑到具有恒定磁场的单位球上的罗宾磁性拉普拉斯式，当罗宾参数趋向于$+\ infty $时，我们显示了最低特征值渐近线的非单调性。
Previous works provided several counterexamples to monotonicity of the lowest eigenvalue for the magnetic Laplacian in the two-dimensional case. However, the three-dimensional case is less studied. We use the results obtained by Helffer, Kachmar and Raymond to provide one of the first counterexamples in 3D. Considering the Robin magnetic Laplacian on the unit ball with a constant magnetic field, we show the non-monotonicity of the lowest eigenvalue asymptotics when the Robin parameter tends to $+\infty$.
