# Regularity of minimizers for a model of charged droplets

## TL;DR

This paper studies the regularity of minimizers in a variational model for charged liquid droplets, incorporating screening effects, and establishes partial regularity results to advance understanding of droplet shapes.

## Contribution

It provides the first partial regularity results for minimizers in a charged droplet model considering screening effects, enhancing theoretical understanding.

## Key findings

- Proved partial regularity of minimizers.
- Incorporated screening effects into the regularity analysis.
- Laid groundwork for further analysis of droplet shapes.

## Abstract

We investigate properties of minimizers of a variational model describing the shape of charged liquid droplets. The model, proposed by Muratov and Novaga, takes into account the regularizing effect due to the screening of free counterionions in the droplet. In particular we prove partial regularity of minimizers, a first step toward the understanding of further properties of minimizers.