# Isoperimetric problems with non-local penalization terms

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Date/heure
Date(s) - 03/06/2014
11 h 00 min - 12 h 00 min

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$The talk will focus on a model arising from the physic problem of describing the$
behaviour of a liquid drop with a charge of $Q>0$. Such a model takes the form
$\min\{ P(E)+Q^2\mathcal{NL}(E): \mathrm{vol}(E)=\mathrm{constant}}\},$
with $P(E)$ being the perimeter of $E\subset \mathbb{R}^N$ and $\mathcal{NL}$ a non-local operator describing the repulsive
effect of the charge. We shall discuss existence issues and qualitative behaviours of minimizers depending
on the value of $Q$ and on the choice of the non-local operator.
We may eventually briefly discuss a similar problem: given a charged closed wire, what shape does it take.
The talk is based on collaborative work with M. Goldman and M. Novaga.
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