Large volume minimizers of a non local isoperimetric problem: theoretical and numerical approaches

Abstract

We consider the volume-constrained minimization of the sum of the perimeter and the Riesz potential. We add an external potential of the form $\Vert x{\Vert }^{\beta }$ that provides the existence of a minimizer for any volume constraint, and we study the geometry of big minimizers. Then we provide a numerical method to adress this variational problem.

This improved version contains some minor modifications, new references, and one extra numerical experiment