Large Volume Minimizers of a Nonlocal Isoperimetric Problem: Theoretical and Numerical Approaches

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

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