Existence of Compactly Supported Global Minimisers for the Interaction Energy View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-09

AUTHORS

José A. Cañizo, José A. Carrillo, Francesco S. Patacchini

ABSTRACT

The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not H-stable, which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the "gaps" it may have. The class of potentials for which we prove the existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. We also show that the support of local minimisers is compact under suitable assumptions. More... »

PAGES

1197-1217

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-015-0852-3

DOI

http://dx.doi.org/10.1007/s00205-015-0852-3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1006835229


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