On the existence of minimizing sets for a weakly-repulsive nonlocal energy

Variational methods for problems in mechanics (70G75) Variational problems in a geometric measure-theoretic setting (49Q20) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Optimization of shapes other than minimal surfaces (49Q10) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Optimality conditions for problems involving relations other than differential equations (49K21)

Cites Work

Regularity of local minimizers of the interaction energy via obstacle problems
On minimizers of interaction functionals with competing attractive and repulsive potentials
Geometry of minimizers for the interaction energy with mildly repulsive potentials
Isoperimetry and stability properties of balls with respect to nonlocal energies
Minimisers of a general Riesz-type problem
Isodiametry, variance, and regular simplices from particle interactions
Minimizers for a one-dimensional interaction energy
Uniqueness and radial symmetry of minimizers for a nonlocal variational problem
From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials
Existence of ground states of nonlocal-interaction energies
Existence of compactly supported global minimisers for the interaction energy
Minimality of balls in the small volume regime for a general Gamow-type functional
Classifying minimum energy states for interacting particles: regular simplices
On an Isoperimetric Problem with a Competing Nonlocal Term I: The Planar Case
On an Isoperimetric Problem with a Competing Nonlocal Term II: The General Case
A Compactness Lemma and Its Application to the Existence of Minimizers for the Liquid Drop Model
Nonlocal Shape Optimization via Interactions of Attractive and Repulsive Potentials
A "liquid-solid" phase transition in a simple model for swarming, based on the "no flat-spots" theorem for subharmonic functions
Classifying Minimum Energy States for Interacting Particles: Spherical Shells
Proof of spherical flocking based on quantitative rearrangement inequalities
A note on some non-local variational problems

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