A free boundary problem associated with the isoperimetric inequality
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2016
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| _version_ | 1866929339643199488 |
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| author | Abanov, Ar. Beneteau, C. Khavinson, D. Teodorescu, R. |
| author_facet | Abanov, Ar. Beneteau, C. Khavinson, D. Teodorescu, R. |
| contents | This paper proves a 30 year old conjecture that disks and annuli are the only domains where analytic content - the uniform distance from $\bar{z}$ to analytic functions - achieves its lower bound. This problem is closely related to several well-known free boundary problems, in particular, Serrin's problem about laminar flow of incompressible viscous fluid for multiply-connected domains, and Garabedian's problem on the shape of electrified droplets. Some further ramifications and open questions, including extensions to higher dimensions, are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1601_03885 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A free boundary problem associated with the isoperimetric inequality Abanov, Ar. Beneteau, C. Khavinson, D. Teodorescu, R. Complex Variables Mathematical Physics Classical Analysis and ODEs 30D05, 30E10, 30E25 This paper proves a 30 year old conjecture that disks and annuli are the only domains where analytic content - the uniform distance from $\bar{z}$ to analytic functions - achieves its lower bound. This problem is closely related to several well-known free boundary problems, in particular, Serrin's problem about laminar flow of incompressible viscous fluid for multiply-connected domains, and Garabedian's problem on the shape of electrified droplets. Some further ramifications and open questions, including extensions to higher dimensions, are also discussed. |
| title | A free boundary problem associated with the isoperimetric inequality |
| topic | Complex Variables Mathematical Physics Classical Analysis and ODEs 30D05, 30E10, 30E25 |
| url | https://arxiv.org/abs/1601.03885 |