Seminario de Análisis y Aplicaciones

Día y hora: 26 de Enero 2014, 11:30-12:30
Lugar: Aula Naranja, ICMAT
Ponente: Joan Verdera (UAB)
Título: Explicit minimisers of non-local energies
Resumen: 
Non local energies appear in describing large systems of interacting particles or individuals. The continuous limit of discrete energies leads to expressions of the form

∫ ∫k(x-y)dμ(x) dμ(y)+ ∫|x|²dμ(x)

which have to be minimised on the set of probability measures in ℝ^d . The kernel k is even, homogeneous of degree -(d-2) in ℝ^d and smooth off the origin. Under the assumption that the Fourier transform of the kernel is positive off the origin and for some dimensions (we cannot cover all cases), one can show that there exists a unique minimiser which is the normalised characteristic function of an ellipsoid centred at the origin and possibly rotated. I will explain how this ellipsoid appears and how you show that the normalised characteristic function of the candidate ellipsoid is indeed the minimiser of the energy. This is joint work with Mateu, Mora, Rondi and Scardia.