On planar Beltrami equations and Hoelder regularity

Abstract

We provide estimates for the Hölder exponent of solutions to the Beltrami equation $\dbar f=μ\de f+ν\bar{\de f}$, where the Beltrami coefficients $μ,ν$ satisfy $\||μ|+|ν|\|_\infty<1$ and $\Im(ν)=0$. 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&#34; type, on which our estimates are actually attained, and we discuss the main properties of such mappings.