%0 Journal Article
%T On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues
%A Alexandre Girouard
%A Iosif Polterovich
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0808.2968v2