Let $\mathcal {QC}(K, g) $ be a family of $ K $-quasiconformal mappings of the open unit
disk onto itself satisfying the PDE $\Delta w= g $, $ g\in C (\overline {\mathbb {U}}) $, $ w …

In this paper, we investigate solutions of the hyperbolic Poisson equation Δ _ hu (x)= ψ (x) Δ
hu (x)= ψ (x), where ψ ∈ L^ ∞ (B^ n,\mathbb R^ n) ψ∈ L∞(B n, R n) and Δ _ hu (x)=(1-| x …

We prove a global estimate for the gradient of the solution of the Poisson differential
inequality| Δ u (x)|≤ a| Du (x)| 2+ b, x∈ B n, where a, b<∞ and u| _ S^ n-1 ∈ C^ 1, α (S^ n …

In [22], Pavlovic proved that the quasiconformality of harmonic homeomorphisms between D
can be characterized in terms of their bi-Lipschitz continuity ([22, Theorem 1.2]). See …

We prove the following theorem: every quasiconformal harmonic mapping between two
plane domains with C1, α (α< 1) and, respectively, C1, 1 compact boundary is bi-Lipschitz …

In this paper, we establish the Hölder continuity of hyperbolic Poisson integral and
hyperbolic Green integral, respectively. Firstly, we prove that the mapping u= G h [ψ] is …

Representation formula and bi-Lipschitz continuity of solutions to inhomogeneous biharmonic
Dirichlet problems in the unit disk - ScienceDirect Skip to main contentSkip to article Elsevier …

In this paper, our main aim is to discuss the properties of harmonic mappings in the unit ball
𝔹n. First, we characterize the harmonic Bloch spaces and the little harmonic Bloch spaces …

In\cite {kamz} the author proved that every quasiconformal harmonic mapping between two
Jordan domains with $ C^{1,\alpha} $, $0<\alpha\le 1$, boundary is bi-Lipschitz, providing …

We obtain a sharp estimate of the derivatives of harmonic quasiconformal extension u= P
[phi] of a Lipschitz map phi: Sn-1-> Rn. We also consider additional conditions which …