Optimal regularity for planar mappings of finite distortion

Details Optimal regularity for planar mappings of finite distortion Optimal regularity for planar mappings of finite distortion

2008-01-30

arxiv.org/abs/0801.4624v2

Mathematics

Complex Variables

22 pages, formula (3) has been corrected

Scientific paper

Let $f:\Omega\to\IR^2$ be a mapping of finite distortion, where $\Omega\subset\IR^2 .$ Assume that the distortion function $K(x,f)$ satisfies $e^{K(\cdot, f)}\in L^p_{loc}(\Omega)$ for some $p>0.$ We establish optimal regularity and area distortion estimates for $f$. Especially, we prove that $|Df|^2 \log^{\beta -1}(e + |Df|) \in L^1_{loc}(\Omega) $ for every $\beta

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