On quasiregular mappings between smooth Jordan domains

It is proved that every proper quasiregular C2 mapping w between two plane Jordan domains Ω∈C1,α and G∈C2,α, 0<α⩽1, satisfying the differential inequality |Δw|⩽M2|∇w|+N is Lipschitz continuous. This extends the main result of the author and M. Mateljević (Kalaj and Mateljević, 2006 [7]).