论文标题
在平面外部域中的扰动的罗宾双拉乳光度的等等不平等现象
An isoperimetric inequality for the perturbed Robin bi-Laplacian in a planar exterior domain
论文作者
论文摘要
在本文中，我们介绍了有限的简单连接的$ C^2 $ -SMOTH OPEN套装的外观上的二维Robin Bi-Laplacian。所考虑的扰动是较低的，对应于张力。我们证明，该操作员的基本频谱与正半轴一致，并且当边界参数为负时，负离散频谱是非空的。作为主要结果，我们获得了这种扰动的Robin Bi-Laplacian的最低特征值的等值不平等，在边界最大值的约束下，在边界曲率上设置的有界凸面平面的外部具有负边界参数，而最大值是DISK的外部。在以下假设的情况下证明了等等的不等式，即磁盘外部的最低特征值对应于径向特征功能。我们就张力参数和磁盘的半径提供了足够的条件，以使该属性持有。
In the present paper we introduce the perturbed two-dimensional Robin bi-Laplacian in the exterior of a bounded simply-connected $C^2$-smooth open set. The considered perturbation is of lower order and corresponds to tension. We prove that the essential spectrum of this operator coincides with the positive semi-axis and that the negative discrete spectrum is non-empty if, and only if, the boundary parameter is negative. As the main result, we obtain an isoperimetric inequality for the lowest eigenvalue of such a perturbed Robin bi-Laplacian with a negative boundary parameter in the exterior of a bounded convex planar set under the constraint on the maximum of the curvature of the boundary with the maximizer being the exterior of the disk. The isoperimetric inequality is proved under the additional assumption that to the lowest eigenvalue for the exterior of the disk corresponds a radial eigenfunction. We provide a sufficient condition in terms of the tension parameter and the radius of the disk for this property to hold.
