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From Neumann to Steklov and beyond, via Robin: The Weinberger way
American Journal of Mathematics ( IF 1.7 ) Pub Date : 2021-06-08
Pedro Freitas, Richard S. Laugesen

abstract:

The second eigenvalue of the Robin Laplacian is shown to be maximal for the ball among domains of fixed volume, for negative values of the Robin parameter $\alpha$ in the regime connecting the first nontrivial Neumann and Steklov eigenvalues, and even somewhat beyond the Steklov regime. The result is close to optimal, since the ball is not maximal when $\alpha$ is sufficiently large negative, and the problem admits no maximiser when $\alpha$ is positive.



中文翻译:

从诺依曼到斯泰克洛夫及其他,通过罗宾:温伯格方式

摘要:

Robin Laplacian 的第二个特征值对于固定体积域中的球来说是最大的,对于连接第一个非平凡 Neumann 和 Steklov 特征值的区域中 Robin 参数 $\alpha$ 的负值,甚至有点超出 Steklov政权。结果接近最优,因为当 $\alpha$ 足够大为负时球不是最大的,当 $\alpha$ 为正时,问题不承认最大化。

更新日期:2021-06-08
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