On planar Beltrami equations and Hoelder regularity

Details On planar Beltrami equations and Hoelder regularity On planar Beltrami equations and Hoelder regularity

2006-12-15

arxiv.org/abs/math/0612438v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

We provide estimates for the H\"older exponent of solutions to the Beltrami equation $\dbar f=\mu\de f+\nu\bar{\de f}$, where the Beltrami coefficients $\mu,\nu$ satisfy $\||\mu|+|\nu|\|_\infty<1$ and $\Im(\nu)=0$. Our estimates depend on the arguments of the Beltrami coefficients as well as on their moduli. Furthermore, we exhibit a class of mappings of the ``angular stretching" type, on which our estimates are actually attained, and we discuss the main properties of such mappings.

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