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arXiv · 1612.09233

Discrete minimisers are close to continuum minimisers for the interaction energy

J. A. Cañizo·F. S. Patacchini
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Abstract

Under suitable technical conditions we show that minimisers of the discrete interaction energy for attractive-repulsive potentials converge to minimisers of the corresponding continuum energy as the number of particles goes to infinity. We prove that the discrete interaction energy $\Gamma$-converges in the narrow topology to the continuum interaction energy. As an important part of the proof we study support and regularity properties of discrete minimisers: we show that continuum minimisers belong to suitable Morrey spaces and we introduce the set of empirical Morrey measures as a natural discrete analogue containing all the discrete minimisers.

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J. A. Cañizo, F. S. Patacchini. 2016-12-29. Discrete minimisers are close to continuum minimisers for the interaction energy. https://doi.org/10.1007/s00526-017-1289-3

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