On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
复制标题
DOI：
10.1007/s10688-010-0014-1
复制
发表时间：
2008-08
影响因子：
0.4
通讯作者：
A. Girouard;I. Polterovich
中科院分区：
文献类型：
--
作者：
A. Girouard;I. Polterovich
We prove that the Hersch-Payne-Schiffer isoperimetric inequality for thenth nonzero Steklov eigenvalue of a bounded simply connected planar domain is sharp for alln⩾ 1. The equality is attained in the limit by a sequence of simply connected domains degenerating into a disjoint union ofnidentical disks. Similar results are obtained for the product of two consecutive Steklov eigenvalues. We also give a new proof of the Hersch-Payne-Schiffer inequality forn= 2 and show that it is strict in this case.
