For K >= 1, suppose that f is a K-quasiconformal self-mapping of the unit disk D, which satisfies the following: (1) the biharmonic equation Delta(Delta f) = g (g is an element of C((D) over bar)), (2) the boundary condition Delta f = phi(phi is an element of C(T) and T denotes the unit circle), (3) f (0) = 0. The purpose of this paper is to prove that f is Lipschitz continuous, and, further, it is bi-Lipschitz continuous if parallel to g parallel to(infinity) and parallel to phi parallel to(infinity) are small enough. Moreover, the estimates are asymptotically sharp as K -> 1 , parallel to g ...
