Calculus of Variations and Geometric Measure Theory

Variational methods and applications

On the existence and regularity of minimizers of attraction-repulsion energies

Aldo Pratelli (University of Pisa)

created by paolini on 08 Sep 2021
modified on 14 May 2022

10 sep 2021 -- 11:30   [open in google calendar]


Since Gamow introduced the celebrated liquid drop model, in the 1930's, there has been a deep interest between Physics and Mathematics on the minimization of various forms of energy, usually showing the so-called attraction-repulsion effect, that is, particles attract each other if they are far away, but they repulse each other when they become too close. There have been in the decades, and particularly in the last years, severals specific examples and generalizations. In this talk, we aim to give an overall view of some of the main problems, discussing known properties and open questions. We will range from classical results to very recent ones. Some of the results are obtained in different collaborations with D. Carazzato, N. Fusco, and M. Novaga.