1. CJM Online first
|Beltrami Equation with Coefficient in Sobolev and Besov Spaces|
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, CalderÃ³n-Zygmund operators
Categories:30C62, 35J99, 42B20
2. CJM 2008 (vol 60 pp. 721)
|Uniform Linear Bound in Chevalley's Lemma |
We obtain a uniform linear bound for the Chevalley function at a point in the source of an analytic mapping that is regular in the sense of Gabrielov. There is a version of Chevalley's lemma also along a fibre, or at a point of the image of a proper analytic mapping. We get a uniform linear bound for the Chevalley function of a closed Nash (or formally Nash) subanalytic set.
Keywords:Chevalley function, regular mapping, Nash subanalytic set
Categories:13J07, 32B20, 13J10, 32S10