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On boundary correspondences under quasiconformal harmonic mappings between smooth Jordan domains
Author(s) -
Kalaj David
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910053
Subject(s) - mathematics , boundary (topology) , unit disk , lipschitz continuity , mathematical analysis , domain (mathematical analysis) , constant (computer programming) , harmonic , harmonic function , pure mathematics , quasiconformal mapping , lipschitz domain , boundary values , function (biology) , characterization (materials science) , unit (ring theory) , hilbert transform , boundary value problem , physics , materials science , quantum mechanics , evolutionary biology , computer science , biology , programming language , nanotechnology , statistics , mathematics education , spectral density
A quantitative version of an inequality obtained in [8, Theorem 2.1] is given. More precisely, for normalized K quasiconformal (q.c.) harmonic mappings of the unit disk onto a Jordan domain Ω ∈ C 1, μ (0 < μ ≤ 1), we give an explicit Lipschitz constant depending on the structure of Ω and on K . In addition, we give a characterization of q.c. harmonic mappings of the unit disk onto an arbitrary Jordan domain with C 2, α boundary in terms of the boundary function using the Hilbert transform. Moreover, a sharp explicit quasiconformal constant is given in terms of the boundary function.