Beltrami Equation with Coefficient in Sobolev and Besov Spaces

Cruz, Victor ; Mateu, Joan ; Orobitg, Joan

Canadian journal of mathematics, Tome 65 (2013) no. 6, pp. 1217-1235

Résumé

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 $X(\mathbb{C})$ .

Détail

DOI : 10.4153/CJM-2013-001-7

Mots-clés : 30C62, 35J99, 42B20, quasiregular mappings, Beltrami equation, Sobolev spaces, Calderón-Zygmund operators

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