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Beltrami Equation with Coefficient in Sobolev and Besov Spaces

Published online by Cambridge University Press:  20 November 2018

Victor Cruz ,
Joan Mateu  and
Joan Orobitg
Victor Cruz
Affiliation:
Instituto de Física y Matemáticas, Universidad Tecnológica de la Mixteca, 69000 Huajuapan de León, Oaxaca, México, e-mail: victorcruz@mixteco.utm.mx
Joan Mateu
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, e-mail: mateu@mat.uab.catorobitg@mat.uab.cat
Joan Orobitg
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, e-mail: mateu@mat.uab.catorobitg@mat.uab.cat
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Abstract

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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, $\bar{\partial }f(z)\,=\,\mu (z)\partial f(z)$, have first derivatives locally in $X(\mathbb{C})$, provided that the Beltrami coefficient $\mu $ belongs to $X(\mathbb{C})$.

Keywords

30C6235J9942B20quasiregular mappingsBeltrami equationSobolev spacesCalderón-Zygmund operators
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 6 , 01 December 2013 , pp. 1217 - 1235
Copyright
Copyright © Canadian Mathematical Society 2013

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