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On the Hersch–payne–schiffer Inequalities for Steklov Eigenvalues
| Content Provider | Semantic Scholar |
|---|---|
| Author | Girouard, Alexandre Polterovich, Iosif |
| Copyright Year | 2008 |
| 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. 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/0808.2968v2.pdf |
| Alternate Webpage(s) | http://www.dms.umontreal.ca/~iossif/steklov.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Abnormal degeneration Eigenvalue Isoperimetric inequality Poincaré–Steklov operator Social inequality |
| Content Type | Text |
| Resource Type | Article |
