  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.
