Discrete minimisers are close to continuum minimisers for the interaction energy
| Autor: | Francesco S. Patacchini, José A. Cañizo |
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| Rok vydání: | 2018 |
| Předmět: |
Continuum (topology)
Applied Mathematics media_common.quotation_subject 010102 general mathematics Mathematical analysis Interaction energy Infinity 01 natural sciences 010101 applied mathematics Mathematics - Analysis of PDEs FOS: Mathematics 0101 mathematics Analysis Energy (signal processing) Topology (chemistry) Analysis of PDEs (math.AP) Mathematics media_common |
| Zdroj: | Calculus of Variations and Partial Differential Equations. 57 |
| ISSN: | 1432-0835 0944-2669 |
| Popis: | 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. Comment: 37 pages, 1 figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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