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Landau's theorem for p-harmonic mappings in several variables

Sh. Chen, S. Ponnusamy, X. Wang (2012)

Annales Polonici Mathematici

A 2p-times continuously differentiable complex-valued function f = u + iv in a domain D ⊆ ℂ is p-harmonic if f satisfies the p-harmonic equation Δ p f = 0 , where p (≥ 1) is a positive integer and Δ represents the complex Laplacian operator. If Ω ⊂ ℂⁿ is a domain, then a function f : Ω m is said to be p-harmonic in Ω if each component function f i (i∈ 1,...,m) of f = ( f , . . . , f m ) is p-harmonic with respect to each variable separately. In this paper, we prove Landau and Bloch’s theorem for a class of p-harmonic mappings f from...

Latent roots of lambda-matrices, Kronecker sums and matricial norms

José S. L. Vitória (1980)

Aplikace matematiky

Kronecker sums and matricial norms are used in order to give a method for determining upper bounds for A where A is a latent root of a lambda-matrix. In particular, upper bounds for z are obtained where z is a zero of a polynomial with complex coefficients. The result is compared with other known bounds for z .

Lebesgue measure and mappings of the Sobolev class W 1 , n

O. Martio (1995)

Banach Center Publications

We present a survey of the Lusin condition (N) for W 1 , n -Sobolev mappings f : G n defined in a domain G of n . Applications to the boundary behavior of conformal mappings are discussed.

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