Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

In this seminar we present some recent results regarding density estimates for level sets of minimizers of local and nonlocal energies, which arise from phase separation problems, such as the Ginzburg-Landau energy functional. In particular, we prove density estimates when the phase separation is induced by a double-well potential which presents a slow growth from the pure phases. As a byproduct, we obtain the uniform convergence of the interfaces of any sequence of minimizers of a suitably rescaled energy functional to a set with Hausdorff codimension one.