Regularity of minimisers for a model of charged droplets

We investigate properties of minimisers of a variational model describing the shape of charged liquid droplets. Roughly speaking, the shape of a charged liquid droplet is determined by the competition between an ”aggerating” term, due to surface tension forces, and to a ”disaggergating” term due to the repulsive effect between charged particles.

In my talk I want to present our ”first” analysis of the so called Deby-Hückel-type free energy. In particular we show that minimisers satisfy a partial regularity result, a first step of understanding the further properties of a minimiser. The presented results are joint work with Guido De Philippis and Giulia Vescovo.