Discrete minimisers are close to continuum minimisers for the interaction energy

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• Francesco Saverio Paracchini (Imperial College)
• Monday 06 March 2017, 15:00-16:00
• CMS, MR13.

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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 weak topology to the continuum interaction energy. As part of the proof we study regularity properties of 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. This is joint work with José Alfredo Cañizo.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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