On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues

Alexandre Girouard; Iosif Polterovich

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arXiv · 0808.2968

On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues

Alexandre Girouard·Iosif Polterovich

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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.

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BibTeX RIS

Alexandre Girouard, Iosif Polterovich. 2008-11-16. On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues. https://arxiv.org/abs/0808.2968

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