RESEARCH IN RESIDENCE — Numerical methods for non-local isoperimetric problems

We would like to tackle the numerical resolution of some isoperimetric problems involving non-local competing energies of different nature. The competing energy we consider would either be inspired by Gamow’s liquid drop model for the atomic nucleus (e.g., given by the self-interaction of a set with respect to a general G, or by a fractional perimeter) or would be of Optimal-Transport type (e.g., involving the Wasserstein distances between measures). Although these problems have already been studied theoretically in some regimes, there are many interesting regimes for which little is known ; only some conjectures were formulated. We want to investigate numerically these problems to test these conjectures or formulate new ones.