QUASICONFORMAL HARMONIC MAPPINGS BETWEEN DINI-SMOOTH JORDAN DOMAINS

摘要

Let D and Omega be Jordan domains with Dini-smooth boundaries. We prove that if f : D -> Omega is a harmonic homeomorphism and f is quasiconformal, then f is Lipschitz. This extends some recent results, where stronger assumptions on the boundary are imposed. Our result is optimal in that it coincides with the best condition for Lipschitz behavior of conformal mappings in the plane and conformal parametrizations of minimal surfaces.