Logarithmic capacity is not subadditive – a fine topology approach

Pavel Pyrih

Displaying similar documents to “Logarithmic capacity is not subadditive – a fine topology approach”

Fine topology and quasilinear elliptic equations

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It is shown that the $(1, p)$ -fine topology defined via a Wiener criterion is the coarsest topology making all supersolutions to the $p$ -Laplace equation $div (| \nabla u |^{p - 2} \nabla u) = 0$ continuous. Fine limits of quasiregular and BLD mappings are also studied.

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Biholomorphic invariance of capacity and the capacity of an annulus

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Choquet integrals in potential theory.

David R. Adams (1998)

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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...