标题： 半经典特征值估计在磁性台阶下（原标题：在半经典极限下听取磁性边缘的形状） 显示英文标题

标题： Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit)

摘要： 我们建立了狄利克雷磁 Laplacian 的准确特征值渐近，并作为副产品，得到了两个连续特征值之间的分裂的精确估计，该磁 Laplacian 具有沿光滑曲线具有跳跃间断性的非均匀磁场。 渐近在半经典极限下成立，这同样对应于大磁场极限，并且在间断曲线的曲率上满足一个几何假设。 显示英文摘要

摘要： We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues, for the Dirichlet magnetic Laplacian with a non-uniform magnetic field having a jump discontinuity along a smooth curve. The asymptotics hold in the semiclassical limit which also corresponds to a large magnetic field limit, and is valid under a geometric assumption on the curvature of the discontinuity curve.