JournalsaihpcVol. 32, No. 6pp. 1283–1305

On minimizers of interaction functionals with competing attractive and repulsive potentials

  • Razvan C. Fetecau

    Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada

  • Ihsan Topaloglu

    Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada

  • Rustum Choksi

    Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada
On minimizers of interaction functionals with competing attractive and repulsive potentials cover
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Abstract

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.

Cite this article

Razvan C. Fetecau, Ihsan Topaloglu, Rustum Choksi, On minimizers of interaction functionals with competing attractive and repulsive potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 6, pp. 1283–1305

DOI 10.1016/J.ANIHPC.2014.09.004