Heinz-type inequality and bi-Lipschitz continuity for quasiconformal mappings satisfying inhomogeneous biharmonic equations

摘要

Let Hom+(T) be the class of all sense-preserving homeomorphic self-mappings of T={z=x+iy is an element of C:|z|=1}. The aim of this paper is twofold. First, we obtain Heinz-type inequality for (K,K ')-quasiconformal mappings satisfying inhomogeneous biharmonic equation Delta(Delta omega) = g in unit disk D with associated boundary value conditions Delta omega|T=phi is an element of C(T) and omega|T=f*is an element of Hom+(T). Second, we establish biLipschitz continuity for (K,K ')-quasiconformal mappings satisfying aforementioned inhomogeneous biharmonic equation when K ',||phi||infinity:=supz is an element of D|phi(z)| and ||g||infinity:=supz is an element of D|g(z)| are small enough.