Extremal Problems in Logarithmic Potential Theory
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.
English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 9, pp 1471-1491.
Citation Example: Latyshev A. A., Zorii N. V. Extremal Problems in Logarithmic Potential Theory // Ukr. Mat. Zh. - 2002. - 54, № 9. - pp. 1220-1236.