On the multi-cell formula in homogenization

par Matthias Ruf (University of Giessen)

lundi 29 juin 2026, 14:00 → 15:00 Europe/Paris

Salle de réunion (Carmes)

Homogenization is by now a classical method to simplify models featuring fine microstructure. In the case of integral functionals on Sobolev spaces, the form of simplification depends drastically on whether the integrand is convex or not. For non-convex integrands, the homogenized integrand is given by a complicated multi-cell involving a minimization problem on larger and larger cubes. In this talk, we present a method that allows us to restrict the minimization problem to smaller classes (e.g., more regular functions beyond density in energy). We then illustrate how this strategy can help in a variational analysis.
This is based on joint work with Annika Bach (TU Eindhoven).