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# Beltrami Equation with Coefficient in Sobolev and Besov Spaces

Published:2013-02-06
Printed: Dec 2013
• Victor Cruz,
Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, 69000 Huajuapan de León, Oaxaca, México
• Joan Mateu,
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia
• Joan Orobitg,
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia
 Format: LaTeX MathJax PDF

## Abstract

Our goal in this work is to present some function spaces on the complex plane $\mathbb C$, $X(\mathbb C)$, for which the quasiregular solutions of the Beltrami equation, $\overline\partial f (z) = \mu(z) \partial f (z)$, have first derivatives locally in $X(\mathbb C)$, provided that the Beltrami coefficient $\mu$ belongs to $X(\mathbb C)$.
 Keywords: quasiregular mappings, Beltrami equation, Sobolev spaces, Calderón-Zygmund operators
 MSC Classifications: 30C62 - Quasiconformal mappings in the plane 35J99 - None of the above, but in this section 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)

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