Extremal Problems in Logarithmic Potential Theory

Authors

  • N. V. Zorii
  • A. A. Latyshev

Abstract

We pose and solve an extremal problem of logarithmic potential theory that is dual to the main minimum problem in the theory of interior capacities of condensers but, in contrast to the latter, it is solvable even in the case of a nonclosed condenser. Its solution is a natural generalization of the classical notion of interior equilibrium measure of a set. A condenser is treated as a finite collection of signed sets such that the closures of sets with opposite signs are pairwise disjoint. We also prove several assertions on the continuity of extremals.

Published

25.09.2002

Issue

Section

Research articles

How to Cite

Zorii, N. V., and A. A. Latyshev. “Extremal Problems in Logarithmic Potential Theory”. Ukrains’kyi Matematychnyi Zhurnal, vol. 54, no. 9, Sept. 2002, pp. 1220-36, https://umj.imath.kiev.ua/index.php/umj/article/view/4161.