Displaying similar documents to “Fine topology and quasilinear elliptic equations”

Plurifine potential theory

Jan Wiegerinck (2012)

Annales Polonici Mathematici

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We give an overview of the recent developments in plurifine pluripotential theory, i.e. the theory of plurifinely plurisubharmonic functions.

On the axiomatic of harmonic functions II

Corneliu Constantinescu, A. Cornea (1963)

Annales de l'institut Fourier

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On démontre dans l’axiomatique de M. Brelot la linéarité de l’opération de balayage appliquée aux fonctions surharmoniques en utilisant seulement les axiomes 1, 2, 3, l’espace de base n’ayant pas nécessairement une base dénombrable.

Perturbation of harmonic structures and an index-zero theorem

Bertram Walsh (1970)

Annales de l'institut Fourier

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In the framework of an axiomatic theory of sheaves of “harmonic” functions, a notion of perturbation of these sheaves is introduced which corresponds to the replacement of the operator Δ by an operator Δ + f , in the classical situation. The “harmonic” functions with which the paper is concerned are assumed to satisfy certain hypotheses (weaker than the axioms of Bauer); it is shown that the perturbed harmonic functions also satisfy these hypotheses. Moreover, the results obtained imply that...

Logarithmic capacity is not subadditive – a fine topology approach

Pavel Pyrih (1992)

Commentationes Mathematicae Universitatis Carolinae

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In Landkof’s monograph [8, p. 213] it is asserted that logarithmic capacity is strongly subadditive, and therefore that it is a Choquet capacity. An example demonstrating that logarithmic capacity is not even subadditive can be found e.gi̇n [6, Example 7.20], see also [3, p. 803]. In this paper we will show this fact with the help of the fine topology in potential theory.