Suppose that f satisfies the following: ( 1 ) the polyharmonic equation Δ m f = Δ ( Δ m − 1 f ) = φ m ( φ m ∈ C ( B n ¯ , R n ) ) , (2) the boundary conditions Δ 0 f = φ 0 , Δ 1 f = φ 1 , … , Δ m − 1 f = φ m − 1 on S n − 1 ( φ j ∈ C ( S n − 1 , R n ) for j ∈ { 0 , 1 , … , m − 1 } and S n − 1 denotes the boundary of the unit ball B n ), and ( 3 ) f ( 0 ) = 0 , where n ≥ 3 and m ≥ 1 are integers. Initially, we prove a Schwarz type lemma and use it to obtain a Heinz type inequality of mappings satisfying the polyharmonic...
