The aim of the paper is to introduce the new functional, which is defined on vector compact sets. The functional has the extremal point on the support of the equilibrium measure for vector extremal logarithmic potential problem with an external field and Angelesko matrix of interaction. We will show how to use the functional by extremal problem for two intervals with common endpoint.

vector logarithmic potential, external field, Angelesko System

Theoretical and applied problems of mechanics