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Beltrami Equation with Coefficient in Sobolev and Besov Spaces |
20 pages
Published:2013-02-06
- Victor Cruz,
- Joan Mateu,
- Joan Orobitg,
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.) |