Seminario de Ecuaciones Diferenciales – Francesco Patacchini

Detalles de Evento

• Inicio: 29 septiembre 2015 12:30
• Lugar de encuentro: Seminario 1ª planta
• Categorías: ,
• Institution: Imperial College
• Room: Seminario 1ª planta
• Organizer: David Ruiz
• Host: José A. Cañizo

Title: Existence of compactly supported global minimisers for the interaction energy
Speaker: Francesco Patacchini, Imperial College (UK)
Abstract: We show the existence of compactly supported global minimisers under almost optimal hypotheses for continuum models of particles interacting through a potential. The main assumption on the potential is that it is catastrophic, or not H-stable, which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the gaps'' it may have. The class of potentials for which we prove existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. This is a joint work with J. A. Cañizo and J. A. Carrillo.
1 de octubre, 12:30, Seminario 1ª planta IEMath-GR