论文标题
罗宾拉普拉斯在域上的光谱优化，该域名接收平行坐标
Spectral optimization for Robin Laplacian on domains admitting parallel coordinates
论文作者
论文摘要
在本文中，我们处理对平行坐标的平面域家族的Robin Laplacian的光谱优化，即在光滑的闭合曲线上建造的固定宽度条，以及具有光滑边界的凸面集的外部。我们表明，如果保持曲线长度固定，则指代固定宽度条的第一个特征值是针对通过圆形环的最大化的罗宾参数的任何值。此外，我们证明，与负robin参数相对应的凸域$ω$外部的第二个特征值不会超过磁盘的类似数量，该磁盘的边界的曲率大于或等于$ \partialΩ$的最大值的曲率。
In this paper we deal with spectral optimization for the Robin Laplacian on a family of planar domains admitting parallel coordinates, namely a fixed-width strip built over a smooth closed curve and the exterior of a convex set with a smooth boundary. We show that if the curve length is kept fixed, the first eigenvalue referring to the fixed-width strip is for any value of the Robin parameter maximized by a circular annulus. Furthermore, we prove that the second eigenvalue in the exterior of a convex domain $Ω$ corresponding to a negative Robin parameter does not exceed the analogous quantity for a disk whose boundary has a curvature larger than or equal to the maximum of that for $\partialΩ$.
