published on April 12, 2024
The Klein-Gordon equation on asymptotically flat spacetimes
By Dean Baskin
Explicit minimizers for a class of nonlocal interaction energies
Appears in collection : Beyond Elasticity: Advances and Research Challenges / Au-delà de l'élasticité : avancées dans la recherche et prochains défis
Nonlocal interaction energies are continuum models for large systems of particles, where typically each particle interacts not only with its immediate neighbors, but also with particles that are far away. Examples of these energies arise in many different applications, such as biology (population dynamics), physics (Ginzburg-Landau vortices), and material science (dislocation theory). A fundamental question is understanding the optimal arrangement of particles at equilibrium, which are described, at least in average, by minimizers of the energy. In this talk I will focus on a class of nonlocal energies that are perturbations of the Coulomb energy and I will show how their minimizers can be explicitly characterized. This is based on joint works with J. Mateu, L. Rondi, L. Scardia, and J. Verdera.
