Abstract
We prove that !u( ) ≤ C!f ( ), where u : Ω → R n is the harmonic extension of a continuous map f : @Ω → R n , if u is a K-quasiregular map and Ω is bounded in R n with C 2 boundary. Here C is a constant depending only on n, !f and K and !h denotes the modulus of continuity of h. We also prove a version of this result for Λ!-extension domains with c-uniformly perfect boundary and quasiconformal mappings.
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