AI 中文总结
本文研究Robin型Aharonov-Bohm哈密顿量的正则逼近问题，借助$\u0393$-收敛技术构造含可穿透螺线管的Schrödinger算子族，证明强预解意义下的逼近结果，并推广至一般光滑闭紧曲面与有界磁势场景。
AI 中文摘要
在三维空间$\u211d^3$中，针对Robin参数$L>0$，本文证明存在一族含可穿透环形螺线管与可变电导率的Schrödinger算子，能够逼近在螺线管（边界）处带Robin边界条件的磁性Aharonov-Bohm算子。研究同时表明，先通过光滑势、再在螺线管内部设置势垒的逼近方式会导出Dirichlet边界条件。上述逼近在强预解算子意义下成立，借助$\u0393$-收敛技术得到，且适用于更一般的光滑闭紧曲面以及连续有界磁势的情形。
英文摘要
In the space $\mathbb R^3$, for Robin parameter $L>0$, it is shown that there is a family of Schrödinger operators with penetrable toroidal solenoid and variable conductivity that approximates the magnetic Aharonov-Bohm operator with a Robin boundary condition at the solenoid (border). It is also shown that approximations via smooth potentials and then a barrier in the solenoid interior give Dirichlet boundary conditions. The approximations are in the strong resolvent sense and obtained through the $Γ$-convergence technique, and they hold for the more general setting of smooth, closed and compact surfaces and continuous and bounded magnetic potentials.
CommentsAccepted in Reviews in Mathematical Physics
