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SUMMARY:Shape Optimisation for nonlocal anisotropic energies - Lucia Scard
 ia (Heriot-Watt University)
DTSTART:20250821T130000Z
DTEND:20250821T134500Z
UID:TALK234760@talks.cam.ac.uk
DESCRIPTION:We consider shape optimisation problems for sets of prescribed
  mass\, where the driving energy functional is nonlocal and anisotropic. M
 ore precisely\, we deal with the case of attractive/repulsive interactions
  in two and three dimensions\, where the attraction is quadratic and the r
 epulsion is given by an anisotropic variant of the Coulomb potential.&nbsp
 \;\nUnder the sole assumption of strict positivity of the Fourier transfor
 m of the interaction potential\, we show the existence of a threshold valu
 e for the mass above which the minimiser is an ellipsoid\, and below which
  the minimiser does not exist. If\, instead\, the Fourier transform of the
  interaction potential is only nonnegative\, we show the emergence of a di
 chotomy: either there exists a threshold value for the mass as in the case
  above\, or the minimiser is an ellipsoid for any positive value of the ma
 ss.&nbsp\;\nThis is joint work with Riccardo Cristoferi and Maria Giovanna
  Mora.
LOCATION:Seminar Room 1\, Newton Institute
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