Equilibrium Potentials with External Fields

Abstract

We investigate the Gauss variational problem over fairly general classes of Radon measures in a locally compact space X. We describe potentials of minimizing measures, establish their characteristic properties, and prove the continuity of extremals. Extremal problems dual to the original one are formulated and solved. The results obtained are new even in the case of classical kernels and the Euclidean space \(\mathbb{R}^n \) .