On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
Spectral Theory
2012-02-24 v2 Differential Geometry
Abstract
We prove that the isoperimetric inequality due to Hersch-Payne-Schiffer for the n-th nonzero Steklov eigenvalue of a bounded simply-connected planar domain is sharp for all n=1,2,... The equality is attained in the limit by a sequence of simply-connected domains degenerating to the disjoint union of n identical disks. We give a new proof of this inequality for n=2 and show that it is strict in this case. Related results are also obtained for the product of two consecutive Steklov eigenvalues.
Cite
@article{arxiv.0808.2968,
title = {On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues},
author = {Alexandre Girouard and Iosif Polterovich},
journal= {arXiv preprint arXiv:0808.2968},
year = {2012}
}
Comments
15 pages, 3 figures. Significantly revised version, new title and abstract