Abstract
We use quaternions to solve a certain type of elliptic first-order partial differential equation concerning functions from \(\mathbb{R}^{4}\) to itself. This equation is, in fact, a quaternionic analogue of the general linear Beltrami equation in the plane. The methods used combine Fredholm theory and Fourier multipliers to invert certain types of operators acting on the L p spaces.
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Communicated by Marco M. Peloso.
This article was conceived by the author during a research visit to Syracuse University. I would like to thank the university for the warm welcome and pleasant working conditions, and especially express my gratitude to my advisor, professor Tadeusz Iwaniec, for making the trip possible.
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Koski, A. Quaternionic Beltrami Equations with VMO Coefficients. J Geom Anal 25, 910–923 (2015). https://doi.org/10.1007/s12220-013-9450-5
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DOI: https://doi.org/10.1007/s12220-013-9450-5