Sala Seminari (Dip. Matematica).
The notion of minimizing movement (Almgren-Taylor-Wang, De Giorgi), which has been used to give a general definition of gradient flow (Ambrosio-Gigli-Savaré) can also be used to study a “homogenized” motion for a family of functionals depending on a small parameter. I want to give some simple examples, starting from an elementary ODE, and focus on some types of perimeter functionals in which case the limits describe motion by crystalline mean curvature and some of its non-trivial variants. From those examples we will note that in general the limit motion is not the minimizing movement of the (Gamma-)limit (when it exists), and we will examine some related (open) questions.