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SUMMARY:Discrete minimisers are close to continuum minimisers for the inte
 raction energy - Francesco Saverio Paracchini (Imperial College)
DTSTART:20170306T150000Z
DTEND:20170306T160000Z
UID:TALK71364@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Under suitable technical conditions we show that minimisers of
  the discrete interaction energy for attractive-repulsive potentials conve
 rge to minimisers of the corresponding continuum energy as the number of p
 articles goes to infinity. We prove that the discrete interaction energy G
 amma-converges in the weak topology to the continuum interaction energy. A
 s part of the proof we study regularity properties of minimisers: we show 
 that continuum minimisers belong to suitable Morrey spaces and we introduc
 e the set of empirical Morrey measures as a natural discrete analogue cont
 aining all the discrete minimisers. This is joint work with José Alfredo 
 Cañizo.
LOCATION:CMS\, MR13
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