GT des doctorants ANH et ANEDP
An isoperimetric problem pertubated by an optimal transport term
March 2024
Intervenant : Jules Candau-Tilh
Institution : Université de Lille
Heure : 14h00 - 15h00
Lieu : Salle 3L8

In this ongoing work, I study an isoperimetric problem pertubated by a nonlocal term: given $m>0$, I look for a set $E$ of mass $m$ minimizing the energy $P(E) + \mathcal{W}(E)$, where $P$ is the perimeter and $\mathcal{W}$ is the nonlocal term. To compute $\mathcal{W}$, I solve a variant of the optimal transport problem: given transport cost $c$, I look for a set $F$ not intersecting $E$ whose transport cost from $E$ is a small as possible.

In the talk, I will give an overview of isoperimetric problems and optimal transportation, before presenting some theoretical results and numerical simulation on the $P+\mathcal{W}$ problem.

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