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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 → ℂ m is said to be p-harmonic in Ω if each component function f i (i∈ 1,...,m) of f = ( f ₁ , . . . , 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 → ℝ n defined in a domain G of ℝ n . Applications to the boundary behavior of conformal mappings are discussed.

Letter to the Editor. Remarks on Some Inequalities for Polynomials

Hachani, M. A. (2013)

Mathematica Balkanica New Series

MSC 2010: 30A10, 30C10, 30C80, 30D15, 41A17.In the present article, I point out serious errors in a paper published in Mathematica Balkanica three years ago. These errors seem to go unnoticed because some mathematicians are applying the results stated in this paper to prove other results, which should not continue.

Linear Fractional PDE, Uniqueness of Global Solutions

Schäfer, Ingo, Kempfle, Siegmar, Nolte, Bodo (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 47A60, 30C15.In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.

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