论文标题
磁性拉普拉斯元素的所有自动接合伸展
All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations
论文作者
论文摘要
我们使用边界三联元素在Quasi-Convex域中〜$ω$具有紧凑的边界的所有自相会扩展的参数化，并在$ \ textrm {w}^{1}^{1} _ {\ infty}（\ infty}（\ operlinepline）中。这还为Laplacian在非规范域中的所有自我伴侣扩展提供了新的表征。然后，我们讨论了这种自我偶像扩展的量规变换，并概括了Dirichlet磁性算子对Dirichlet Laplacian的规范等效性的表征；还讨论了与aharonov-bohm效应（包括不规则螺线管）的关系。特别是，在（界）准凸域域的情况下，表明，如果某些扩展是单位等效的（通过平滑的单位函数乘以乘法）到具有零磁电势的实现，那么所有自我聚会实现也是如此。
We use boundary triples to find a parametrization of all self-adjoint extensions of the magnetic Schrödinger operator, in a quasi-convex domain~$Ω$ with compact boundary, and magnetic potentials with components in $\textrm{W}^{1}_{\infty}(\overlineΩ)$. This gives also a new characterization of all self-adjoint extensions of the Laplacian in nonregular domains. Then we discuss gauge transformations for such self-adjoint extensions and generalize a characterization of the gauge equivalence of the Dirichlet magnetic operator for the Dirichlet Laplacian; the relation to the Aharonov-Bohm effect, including irregular solenoids, is also discussed. In particular, in case of (bounded) quasi-convex domains it is shown that if some extension is unitarily equivalent (through the multiplication by a smooth unit function) to a realization with zero magnetic potential, then the same occurs for all self-adjoint realizations.
