SOBOLEV REGULARITY OF QUASICONFORMAL MAPPINGS ON DOMAINS

Consider a Lipschitz domain Omega and a measurable function mu supported in (Omega) over bar with parallel to mu parallel to(L infinity) < 1. Then the derivatives of a quasiconformal solution of the Beltrami equation partial derivative f = mu partial derivative f inherit the Sobolev regularity W-n,W-p(Omega) of the Beltrami coefficient mu as long as Omega is regular enough. The condition obtained is that the outward unit normal vector N of the boundary of the domain is in the trace space, that is, N is an element of B-p,p(n-1/p)(partial derivative Omega).