Abstract
An essentially unique homeomorphic solution to the Beltrami equation with measurable coefficients was found in the 1930s by Morrey. The most well-known proof from the 1960s uses the theory of Calderón–Zygmund and singular integral operators in \(L^p(\mathbb {C})\). We will present an alternative method to solve the Beltrami equation using the Hodge star operator and standard elliptic PDE theory. We will also discuss a different method to prove the regularity of the solution. This approach is partially based on work by Dittmar.
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Acknowledgements
The author would like to thank Mario Bonk for introducing him to the problem and the many helpful discussions. The author was partially supported by NSF grant DMS 1506099.
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Prywes, E. The Hodge star operator and the Beltrami equation. Complex Anal Synerg 8, 8 (2022). https://doi.org/10.1007/s40627-022-00096-1
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DOI: https://doi.org/10.1007/s40627-022-00096-1