Improved Hölder Continuity of Quasiconformal Maps
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866916388865572864 |
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| author | Bongers, Rosemarie |
| author_facet | Bongers, Rosemarie |
| contents | Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give rise to a certain degree of global regularity and Hölder continuity. In this paper, we give improved lower bounds for the Hölder continuity of these maps; the analysis is based on combining the isoperimetric inequality with a study of the length of quasicircles. Furthermore, the extremizers for Hölder continuity are characterized, and some applications are given to solutions to elliptic partial differential equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1803_10756 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Improved Hölder Continuity of Quasiconformal Maps Bongers, Rosemarie Complex Variables Analysis of PDEs Classical Analysis and ODEs 30C62, 26A16 Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give rise to a certain degree of global regularity and Hölder continuity. In this paper, we give improved lower bounds for the Hölder continuity of these maps; the analysis is based on combining the isoperimetric inequality with a study of the length of quasicircles. Furthermore, the extremizers for Hölder continuity are characterized, and some applications are given to solutions to elliptic partial differential equations. |
| title | Improved Hölder Continuity of Quasiconformal Maps |
| topic | Complex Variables Analysis of PDEs Classical Analysis and ODEs 30C62, 26A16 |
| url | https://arxiv.org/abs/1803.10756 |