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ISSN 1088-6850(e) ISSN 0002-9947(p)

On the degenerate Beltrami equation

Author(s): V. Gutlyanskii; O. Martio; T. Sugawa; M. Vuorinen
Journal: Trans. Amer. Math. Soc. 357 (2005), 875-900.
MSC (2000): Primary 30C62
Posted: October 19, 2004
MathSciNet review: 2110425
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Abstract: We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient $\mu(z)$ has the norm $\Vert\mu\Vert _\infty=1.$ Sufficient conditions for the existence of a homeomorphic solution to the Beltrami equation on the Riemann sphere are given in terms of the directional dilatation coefficients of $\mu.$ A uniqueness theorem is also proved when the singular set $\operatorname{Sing} (\mu)$ of $\mu$ is contained in a totally disconnected compact set with an additional thinness condition on $\operatorname{Sing}(\mu).$

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