The paper proves that for Riesz energy minimization on a segment in the field of a repulsive point charge, the equilibrium measure's support is a pair of symmetric intervals, and gives explicit densities for Coulomb and logarithmic cases.
Bilogliadov, Minimum Riesz energy problem on the hyperdisk
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Riesz equilibrium on a ball in the external field of a point charge
The paper proves that for Riesz energy minimization on a segment in the field of a repulsive point charge, the equilibrium measure's support is a pair of symmetric intervals, and gives explicit densities for Coulomb and logarithmic cases.