Mathematics – Classical Analysis and ODEs
Scientific paper
2008-02-08
J. Math. Pures Appl. (9) 91 (2009), no. 4, 402-431
Mathematics
Classical Analysis and ODEs
44 pages, 7 figures, new references, new results
Scientific paper
We discuss a special class of Beltrami coefficients whose associated quasiconformal mapping is bilipschitz. These are of the form the characteristic function of a planar bounded domain with smooth boundary of class C 1+epsilon times a density of class Lip epsilon on the domain. The crucial fact in the argument is the special extracancellation property of even Calderon-Zygmund kernels, namely that they have zero integral on half the unit ball. This property is expressed in a particularly suggestive way and is shown to have far-reaching consequences. The main result may also be viewed as a Lipschitz regularity result for the Beltrami equation, and so for certain planar second order elliptic equations in divergence form.
Mateu Joan
Orobitg Joan
Verdera Joan
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