An Electrostatics Approach to the Determination of Extremal Measures

Abstract

One of the most important aspects of the minimal energy (or induced equilibrium) prob- lem in the presence of an external field - sometimes referred to as the Gauss variation problem - is the determination of the support of its solution (the so-called extremal measure associated with the field). A simple electrostatic interpretation is presented here, which is apparently new and anyway suggests a novel, rather systematic approach to the solution. By way of illustration, the classical results for Jacobi, Laguerre and Freud weights are explicitly recovered by this alternative method.