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A 3G-Theorem for Jordan Domains in ℝ²

Lotfi Riahi (2004)

Colloquium Mathematicae

We prove a new 3G-Theorem for the Laplace Green function G on an arbitrary Jordan domain D in ℝ². This theorem extends the recent one proved on a Dini-smooth Jordan domain.

A class of functions containing polyharmonic functions in ℝⁿ

V. Anandam, M. Damlakhi (2003)

Annales Polonici Mathematici

Some properties of the functions of the form v ( x ) = i = 0 m | x | i h i ( x ) in ℝⁿ, n ≥ 2, where each h i is a harmonic function defined outside a compact set, are obtained using the harmonic measures.

A constant in pluripotential theory

Zbigniew Błocki (1992)

Annales Polonici Mathematici

We compute the constant sup ( 1 / d e g P ) ( m a x S l o g | P | - S l o g | P | d σ ) : P a polynomial in n , where S denotes the euclidean unit sphere in n and σ its unitary surface measure.

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