Mathematics – Analysis of PDEs
Scientific paper
2006-02-06
Mathematics
Analysis of PDEs
9 pages
Scientific paper
We estimate the Hoelder exponent $\alpha$ of solutions to the Beltrami equation $\dbar f=\mu\de f$, where the Beltrami coefficient satisfies $\|\mu\|_\infty<1$. Our estimate improves the classical estimate $\alpha\ge\|K_\mu\|^{-1}$, where $K_\mu=(1+|\mu|)/(1-|\mu|)$, 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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