Discrete minimisers are close to continuum minimisers for the interaction energy View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-02

AUTHORS

J. A. Cañizo, F. S. Patacchini

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 Γ-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 iscrete analogue containing all the discrete minimisers. More... »

PAGES

24

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URI

http://scigraph.springernature.com/pub.10.1007/s00526-017-1289-3

DOI

http://dx.doi.org/10.1007/s00526-017-1289-3

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50 schema:description 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 Γ-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 iscrete analogue containing all the discrete minimisers.
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