Invertible harmonic mappings of the unit disk onto Dini smooth Jordan domains

In this paper we extend Radó-Kneser-Choquet theorem for the mappings with weak homeomorphic Lipschitz boundary function and Dini's smooth boundary but without restriction on the convexity of the image domain, provided that the Jacobian satisfies a certain boundary condition. The proof is based on a recent extension of Radó-Kneser-Choquet theorem by Alessandrini and Nesi [1] and is used the approximation principle.