On Beltrami equations and Hoelder regularity

Tonia Ricciardi

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On Beltrami equations and Hoelder regularity

Tonia Ricciardi

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Abstract

We estimate the Hoelder exponent $α$ of solutions to the Beltrami equation $\dbar f=μ\de f$, where the Beltrami coefficient satisfies $\|μ\|_\infty<1$. Our estimate improves the classical estimate $α\ge\|K_μ\|^{-1}$, where $K_μ=(1+|μ|)/(1-|μ|)$, and it is sharp, in the sense that it is actually attained in a class of mappings which generalize the radial stretchings. Some other properties of such mappings are also provided.

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Tonia Ricciardi. 2006-02-06. On Beltrami equations and Hoelder regularity. https://arxiv.org/abs/math/0602095

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