论文标题
磁性Neumann和Steklov问题Aharonov-bohm磁性电位的磁性不平等问题
Isoperimetric inequalities for the magnetic Neumann and Steklov problems with Aharonov-Bohm magnetic potential
论文作者
论文摘要
我们讨论了具有aharonov-bohm电位的$ \ mathbb r^2 $的有限域上的磁性拉普拉斯元素的等等不平等。当极点周围的电势不是整数时，Neumann和Steklov问题的最低特征值是正面的。我们在Szegö-Weinberger，Brock和Weinstock的经典不平等精神的精神上为最低特征值建立了等级不平等现象，模型域是一个磁盘，其极点位于其中心。我们考虑具有旋转不变的度量的平面中的更一般的域，其中包括球形和双曲线情况。
We discuss isoperimetric inequalities for the magnetic Laplacian on bounded domains of $\mathbb R^2$ endowed with an Aharonov-Bohm potential. When the flux of the potential around the pole is not an integer, the lowest eigenvalue for the Neumann and the Steklov problems is positive. We establish isoperimetric inequalitites for the lowest eigenvalue in the spirit of the classical inequalities of Szegö-Weinberger, Brock and Weinstock, the model domain being a disk with the pole at its center. We consider more generally domains in the plane endowed with a rotationally invariant metric, which include the spherical and the hyperbolic case.
