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Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter
Asymptotic Analysis ( IF 1.1 ) Pub Date : 2020-09-11 , DOI: 10.3233/asy-201642
K. Gittins 1 , B. Helffer 2
Affiliation  

We consider the cases where there is equality in Courant's nodal domain theorem for the Laplacian with a Robin boundary condition on the square. In our previous two papers, we treated the cases where the Robin parameter $h>0$ is large, small respectively. In this paper we investigate the case where $h<0\,$.

中文翻译:

正方形的 Courant-sharp Robin 特征值:负 Robin 参数的情况

我们考虑在正方形上具有 Robin 边界条件的拉普拉斯算子的 Courant 节点域定理中存在相等的情况。在我们之前的两篇论文中,我们分别处理了Robin参数$h>0$大、小的情况。在本文中,我们研究了 $h<0\,$ 的情况。
更新日期:2020-09-11
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