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Abbildungen harmonischer Raüme mit Anwendung auf die Laplace und Wärmeleitungsgleichung

Wolfhard Hansen (1971)

Annales de l'institut Fourier

This paper is devoted to a study of harmonic mappings φ of a harmonic space E ˜ on a harmonic space E which are related to a family of harmonic mappings of E ˜ into E ˜ . In this way balayage in E may be reduced to balayage in E . In particular, a subset A of E is polar if and only if φ - 1 ( A ) is polar. Similar result for thinness. These considerations are applied to the heat equation and the Laplace equation.

Estimation of Green's function on piecewise Dini-smooth bounded Jordan domains

Mohamed Amine Ben Boubaker, Mohamed Selmi (2013)

Colloquium Mathematicae

We establish inequalities for Green functions on general bounded piecewise Dini-smooth Jordan domains in ℝ². This enables us to prove a new version of the 3G Theorem which generalizes its previous version given in [M. Selmi, Potential Anal. 13 (2000)]. Using these results, we give a comparison theorem for the Green kernel of Δ and the Green kernel of Δ - μ, where μ is a nonnegative and exact Radon measure.

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