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arXiv · 1901.07844

Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale

Kari Astala·Martí Prats·Eero Saksman
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Abstract

We study quasiconformal mappings in planar domains $\Omega$ 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 $\partial \Omega$ 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 $\Omega$ for the principal solutions with Beltrami coefficient supported in $\Omega$.

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Kari Astala, Martí Prats, Eero Saksman. 2019-01-23. Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale. https://doi.org/10.1016/j.matpur.2024.04.008

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