论文标题
三角形的最低罗宾特征值的反向等级不平等
Reverse isoperimetric inequality for the lowest Robin eigenvalue of a triangle
论文作者
论文摘要
我们考虑三角形上的拉普拉斯操作员，但符合有吸引力的罗宾边界条件。我们证明，等边三角形是给定区域的所有三角形中最低特征值的局部最大化器，前提是负边界参数的绝对值足够小，仅取决于区域。此外，使用各种试验功能，我们获得了足够的条件，可以在固定区域约束下在大小耦合方面的固定面积约束下的全球最优性。我们还讨论了固定周长的约束。
We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter.
