The Heinz type inequality, Bloch type theorem and Lipschitz characteristic of polyharmonic mappings
نویسندگان
چکیده
Suppose that f satisfies the following: (1) polyharmonic equation Δmf=Δ(Δm−1f) =φm (φm∈C(Bn¯,Rn)), (2) boundary conditions Δ0f=φ0,Δ1f=φ1,…,Δm−1f=φm−1 on Sn−1 (φj∈C(Sn−1,Rn) for j∈{0,1,…,m−1} and denotes of unit ball Bn), (3) f(0)=0, where n≥3 m≥1 are integers. Initially, we prove a Schwarz type lemma use it to obtain Heinz inequality mappings satisfying with above Dirichlet value conditions. Furthermore, establish Bloch theorem equation, which gives an answer open problem in Chen Ponnusamy, (2019). Additionally, show if is K-quasiconformal self-mapping Bn then Lipschitz continuous, constant asymptotically sharp as K→1+ ‖φj‖∞→0+ j∈{1,…,m}.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2023
ISSN: ['0019-3577', '1872-6100']
DOI: https://doi.org/10.1016/j.indag.2023.05.001