This revised and extended edition of a well-established monograph in function theory
contains a study on various function classes on the disc, a number of new results and new or …

Planar harmonic mappings underly the theory of minimal surfaces in three space. The
seminal paper [13] introduced a complex analytic approach for their studies. Ever since this …

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 …

The purpose of this paper is to study the properties of the solutions to the inhomogeneous
biharmonic equations: Δ (Δ f)= g Δ (Δ f)= g, where g: D → CD¯→ C is a continuous function …

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 …

For a given continuous function g:~ D → C g: D¯→ C and a given continuous function ψ:~ T
→ C ψ: T→ C, we establish some Schwarz type Lemmas for mappings f satisfying the PDE …

The main aim of this paper is to study the Lipschitz continuity of certain (K, K^ ′)(K, K′)-
quasiconformal mappings with respect to the distance ratio metric, and the Lipschitz …

Suppose p ≥ 1 p≥ 1, w= PF w= PF is a harmonic mapping of the unit disk\mathbb DD
satisfying F is absolutely continuous and ̇ F ∈ L^ p (0, 2 π) F˙∈ L p (0, 2 π), where ̇ F (e …

We prove that a harmonic diffeomorphism between two Jordan domains with C 2
boundaries is a (K, K′) quasiconformal mapping for some constants K≥ 1 and K′≥ 0 if …

We establish that every K-quasiconformal mapping w of the unit disk DD onto a C 2-Jordan
domain Ω is Lipschitz provided that Δ w∈ L p (DD) for some p> 2. We also prove that if in …