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

Paula Cerejeiras | Zendy; Klaus Gürlebeck | Zendy; Uwe Kähler | Zendy; Helmuth R. Malonek | Zendy

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

Author(s) -

Paula Cerejeiras,

Klaus Gürlebeck,

Uwe Kähler,

Helmuth R. Malonek

Publication year - 2001

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1002

Subject(s) - type (biology) , mathematics , pure mathematics , mathematical analysis , biology , ecology

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 H into C 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 R into R to the quaternionic derivative of a monogenic function.

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