Some minimization problems for mean field models with competing forces
Rupert L. Frank
Ludwig-Maximilians-Universität München; and Munich Center for Quantum Science and Technology, Germany; California Institute of Technology, Pasadena, United States of America
Download Chapter PDF
This book chapter is published open access.
Abstract
We review recent results on three families of minimization problems, defined on subsets of nonnegative functions with fixed integral. The competition between attractive and repulsive forces leads to transitions between parameter regimes, where minimizers exist and where they do not. The problems considered are generalized liquid drop models, swarming models, and generalized Keller–Segel models.