Quasiconformal solutions to elliptic partial differential equations - Kalaj, David (Annales Fennici Mathematici, 2023)
In this paper, we assume that \(G\) and \(Ω\) are two Jordan domains in \(R^n\) with \(C^2\) boundaries, where \(n2\), and prove that every quasiconformal mapping \(fW^2,1+ε_loc \) of \(G\) onto \(Ω\), satisfying the elliptic partial differential inequality \(|L_ A[f]|(\|Df\|^2+|g|)\), with \(gL^p(G)\), where \(p>n\), is Lipschitz continuous. The result is sharp since for \(p=n\), the mapping \(f\) is not necessarily Lipschitz continuous. This extends several results for harmonic quasiconformal mappings.