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An inequality for the Steklov spectral zeta function of a planar domain
| Content Provider | Semantic Scholar |
|---|---|
| Author | Jollivet, Alexandre Sharafutdinov, Vladimir |
| Copyright Year | 2018 |
| Abstract | We consider the zeta function for the Dirichlet–to–Neumann operator of a simply connected planar domain bounded by a smooth closed curve. We prove that, for a xed real s satisfying jsj > 1 and xed length L.@/ of the boundary curve, the zeta function .s/ reaches its unique minimum when is a disk. This result is obtained by studying the di erence .s/ 2 L.@/ 2 s R.s/, where R stands for the classical Riemann zeta function. The di erence turns out to be non-negative for real s satisfying jsj > 1. We prove some growth properties of the di erence as s ! ̇1. Two analogs of these results are also provided. Mathematics Subject Classi cation (2010). Primary: 35R30; Secondary: 35P99. |
| Starting Page | 271 |
| Ending Page | 296 |
| Page Count | 26 |
| File Format | PDF HTM / HTML |
| DOI | 10.4171/JST/196 |
| Volume Number | 8 |
| Alternate Webpage(s) | http://www.math.nsc.ru/~sharafutdinov/files/articles/JST-2018.pdf |
| Alternate Webpage(s) | https://doi.org/10.4171/JST%2F196 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
