The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (255 KB) | Metadata | Table of Contents | ZAA summary
Volume 20, Issue 1, 2001, pp. 17–34
DOI: 10.4171/ZAA/1002

Published online: 2001-03-31

A Quaternionic Beltrami-Type Equation and the Existence of Local Homeomorphic Solutions

Paula Cerejeiras[1], Klaus Gürlebeck[2], Uwe Kähler[3] and H. Malonek[4]

(1) Universidade de Aveiro, Portugal
(2) Bauhaus-Universität Weimar, Germany
(3) Universidade de Aveiro, Portugal
(4) Universidade de Aveiro, Portugal

The paper deals with a quaternionic Beltrami-type equation, which is a very natural generalization of the complex Beltrami equation to higher dimensions. Special attention is paid to the systematic use of the embedding of the set of quaternions $\mathbb H into \mathbb C^2$ and the corresponding application of matrix singular integral operators. The proof of the existence of local homeomorphic solutions is based on a necessary and sufficient criterion, which relates the Jacobian determinant of a mapping from $\mathbb R^4$ into $\mathbb R^4$ to the quaternionic derivative of a monogenic function.

Keywords: Generalized Beltrami equation, quaternions, singular integral operators, homeomorphic solutions, monogenic functions

Cerejeiras Paula, Gürlebeck Klaus, Kähler Uwe, Malonek H.: A Quaternionic Beltrami-Type Equation and the Existence of Local Homeomorphic Solutions. Z. Anal. Anwend. 20 (2001), 17-34. doi: 10.4171/ZAA/1002