Functional characteristics of space condensers: Their properties and relations among them (Q1114046)

let \(\Omega =R^ p\) or \(\Omega =\overline{R^ p}=R^ p\cup \{\infty \}\) and let \(E^+,E^-\subset \Omega\) be non-empty, closed with respect to \(\Omega\), \(\overline{E^+}\cap \overline{E^-}=\emptyset\). The triple \(E=(E^+,E^-,\Omega)\) is called a condenser in \(\Omega\). The author introduces the capacity Cap(E) and expresses Cap(E) via infima of the Newton energy with respect to some classes of charges associated with E. The coincidence of \(Cap(E^+,E^-,R^ p)\) and the 2-modulus of a family of curves which connect \(E^+\) and \(E^-\) in \(R^ p\) is proved. For \(\Omega =\overline{R^ p}\) the same result was obtained earlier by \textit{J. Hesse} [Ark. Mat. 13, 131-144 (1975; Zbl 0302.31009)].