AI 中文总结
研究ℝ²带外尖峰有界区域上强磁场相关的磁Neumann拉普拉斯算子，分析λ→+∞时特征值行为，明确其渐近展开受尖峰锐度和几何影响，主项阶为λ^(2/(q+1))，拓展了前期相关研究。
AI 中文摘要
我们考虑ℝ²中具有外尖峰的有界区域上的磁Neumann拉普拉斯算子，该算子与依赖参数λ的强磁场相关，研究λ趋于+∞时特征值的行为。我们证明其渐近展开受尖峰的锐度q和几何结构影响，主项阶为λ^(2/(q+1))，这是对光滑区域及带角区域上磁Neumann拉普拉斯算子相关前期工作的拓展。
英文摘要
We consider the magnetic Neumann Laplacian on bounded domains in $\mathbb{R}^2$ with outward peaks. The operator is associated with a large magnetic field depending on a parameter $λ$, and we investigate the behaviour of the eigenvalues as $λ$ tends to $+\infty$. We show that their asymptotic expansion is influenced by the sharpness $q$ and geometry of the peak, and that its main term is of order $λ^{\frac{2}{q+1}}$. This is an extension of previous works on magnetic Neumann Laplacians in smooth domains and domains with corners.
Comments22 pages, 4 figures
