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

Let be the class of all sense-preserving homeomorphic self-mappings of . The aim of this paper is twofold. First, we obtain Heinz-type inequality for (K,K′)-quasiconformal mappings satisfying inhomogeneous biharmonic equation Δ(Δω) = g in unit disk with associated boundary value conditions and . Second, we establish biLipschitz continuity for (K,K′)-quasiconformal mappings satisfying aforementioned inhomogeneous biharmonic equation when and are small enough.