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Regularity of minimal sets for a free interface problem

Giulia Vescovo
Institution: 
SISSA
Location: 
A-134
Schedule: 
Friday, December 7, 2018 - 14:00
Abstract: 

We introduce a variational model describing the shape of a liquid charged droplet at the equilibrium, proposed by Muratov and Novaga. Mathematically a charged liquid droplet can be thought as a set of finite perimeter $E \subset \mathbb{R}^n $ with a prescribed volume. The associated Debye-Huckel-type free energy functional is composed by an "aggregating" term due to the surface tension, represented by the perimeter $P(E)$ and by a "disaggregating" term due to the repulsion effect between charged particles. We give a partial regularity result of minimizers in a certain admissible class.

This is a joint work with Guido De Philippis and Jonas Hirsch.

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