Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866916651507646464 |
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| author | Astala, Kari Prats, Martí Saksman, Eero |
| author_facet | Astala, Kari Prats, Martí Saksman, Eero |
| contents | We study quasiconformal mappings in planar domains $Ω$ and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary $\partial Ω$ and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below $1$, the same conditions give global regularity in $Ω$ for the principal solutions with Beltrami coefficient supported in $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_07844 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale Astala, Kari Prats, Martí Saksman, Eero Analysis of PDEs Classical Analysis and ODEs Complex Variables 30C62, 46E35, 30C35, 28A75 We study quasiconformal mappings in planar domains $Ω$ and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary $\partial Ω$ and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below $1$, the same conditions give global regularity in $Ω$ for the principal solutions with Beltrami coefficient supported in $Ω$. |
| title | Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale |
| topic | Analysis of PDEs Classical Analysis and ODEs Complex Variables 30C62, 46E35, 30C35, 28A75 |
| url | https://arxiv.org/abs/1901.07844 |