Schwarz Lemma for mappings satisfying Biharmonic Equations

2020/03/23 by Khalfallah, Adel, Haggui, Fathi, Mhamdi, Mohamed
#35J25 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 31A30 #Secondary: 31A05

paper · doi:10.48550/arxiv.2003.11460

Abstract

In this paper, we establish some Schwarz type lemmas for mappings Φ satisfying the inhomogeneous biharmonic Dirichlet problem Δ(Δ(Φ)) = g in \mathbbD, Φ=f on \mathbbT and ∂_n Φ=h on \mathbbT, where g is a continuous function on \mathbbD, f,h are continuous functions on \mathbbT, where \mathbbD is the unit disc of the complex plane ℂ and \mathbbT=∂ \mathbbD is the unit circle. To reach our aim, we start by investigating some properties of T₂-harmonic functions. Finally, we prove a Landau-type theorem.

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