Abstract
We obtain a sharp estimate of the derivatives of harmonic quasiconformal extension u = P [φ] of a Lipschitz map φ : Sn−1 → R. We also consider additional conditions which provide that u is Lipschitz on the unit ball; in particular, we give characterizations of Lipschitz continuity of u in the planar case and in the upper half space setting. We also answer a question posed by Martio in [OM] and extend this to the case of several variables.
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