Manifolds of quasiconformal mappings and the nonlinear Beltrami equation
Abstract
In this paper we show that the homeomorphic solutions to each nonlinear Beltrami equation ∂z¯f=H(z,∂zf) generate a two-dimensional manifold of quasiconformal mappings FH⊂Wloc1,2(C). Moreover, we show that under regularity assumptions on H, the manifold FH defines the structure function H uniquely.
Main Authors
Format
Articles
Research article
Published
2019
Series
Subjects
Publication in research information system
Publisher
The Hebrew University Magnes Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201912165319Use this for linking
Review status
Peer reviewed
ISSN
0021-7670
DOI
https://doi.org/10.1007/s11854-019-0059-x
Language
English
Published in
Journal d'Analyse Mathématique
Citation
- Astala, K., Clop, A., Faraco, D., & Jääskeläinen, J. (2019). Manifolds of quasiconformal mappings and the nonlinear Beltrami equation. Journal d'Analyse Mathématique, 139(1), 207-238. https://doi.org/10.1007/s11854-019-0059-x
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Additional information about funding
K. A. was supported by Academy of Finland project SA-307333.
A. C. was supported by research grants 2014SGR75 (Generalitat de Catalunya), MTM2016-75390-P and MTM2016-81703-ERC (Gobierno de Espana) and FP7-607647 (European Union).
D. F. was supported by research grant MTM2011-28198 from the Ministerio de Ciencia e Innovación (MCINN), by MINECO: ICMAT Severo Ochoa project SEV-2011-0087, and by the ERC 307179.
J. J. was supported by the ERC 307179 and Academy of Finland (no. 276233).
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