Vladimir GUTLYANSKII, Olli MARTIO, Toshiyuki SUGAWA and Matti VUORINEN

*On the degenerate Beltrami equation*

### Abstract

We study the well-known Beltrami equation under the
assumption that its measurable complex-valued coefficient
$\mu(z)$ has the norm $\|\mu\|_\infty=1.$ We employ the
pointwise angular dilatation coefficients and this leads to
sufficient conditions on $\mu$ which imply the
existence of a self-homeomorphism of $\sphere$ satisfying
the Beltrami equation with $\mu.$
We also consider the uniqueness of solutions.

submission: 30 May 2001

revision: 21 November 2001

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