Weighted estimates for Beltrami equations

We obtain a priori estimates in $L^p(\omega )$ for the generalized Beltrami equation, provided that the coefficients are compactly supported $VMO$ functions with the expected ellipticity condition, and the weight $\omega$ lies in the Muckenhoupt class $A_p$. As an application, we obtain improved regularity for the jacobian of certain quasiconformal mappings.