On minimizers of interaction functionals with competing attractive and repulsive potentials

Choksi, Rustum; Fetecau, Razvan C.; Topaloglu, Ihsan

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 6, pp. 1283-1305.

We consider a family of interaction functionals consisting of power-law potentials with attractive and repulsive parts and use the concentration compactness principle to establish the existence of global minimizers. We consider various minimization classes, depending on the signs of the repulsive and attractive power exponents of the potential. In the special case of quadratic attraction and Newtonian repulsion we characterize in detail the ground state.

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