Displaying similar documents to “Biholomorphic invariance of capacity and the capacity of an annulus”

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.

Existence theorem for n capacities

Marcel Brelot (1954)

Annales de l'institut Fourier

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On sait que la capacité d’un système de n compacts est majorée par la somme des capacités ; on montre ici qu’on peut trouver n compacts de capacités imposées γ i , tels que la réunion ait une capacité majorant Σ γ i - ϵ ( ϵ > 0 donné à l’avance). Ce résultat établi ici dans un espace de Green avec le potentiel de Green était demandé par Choquet qui l’utilise dans sa théorie des capacités.

A general definition of capacity

Makoto Ohtsuka (1975)

Annales de l'institut Fourier

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One gives a general definition of capacity which includes p -capacity, extremal length and a quantity defined by N.G. Meyers.

Equality cases for condenser capacity inequalities under symmetrization

Dimitrios Betsakos, Stamatis Pouliasis (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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It is well known that certain transformations decrease the capacity of a condenser. We prove equality statements for the condenser capacity inequalities under symmetrization and polarization without connectivity restrictions on the condenser and without regularity assumptions on the boundary of the condenser.

Choquet integrals in potential theory.

David R. Adams (1998)

Publicacions Matemàtiques

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This is a survey of various applications of the notion of the Choquet integral to questions in Potential Theory, i.e. the integral of a function with respect to a non-additive set function on subsets of Euclidean n-space, capacity. The Choquet integral is, in a sense, a nonlinear extension of the standard Lebesgue integral with respect to the linear set function, measure. Applications include an integration principle for potentials, inequalities for maximal functions, stability for solutions...

Variable Sobolev capacity and the assumptions on the exponent

Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)

Banach Center Publications

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In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.

The Besov capacity in metric spaces

Juho Nuutinen (2016)

Annales Polonici Mathematici

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We study a capacity theory based on a definition of Hajłasz-Besov functions. We prove several properties of this capacity in the general setting of a metric space equipped with a doubling measure. The main results of the paper are lower bound and upper bound estimates for the capacity in terms of a modified Netrusov-Hausdorff content. Important tools are γ-medians, for which we also prove a new version of a Poincaré type inequality.