# Perturbations of variational evolutions

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Andrea Braides
(Dip. Mat. Univ. Roma ``Tor Vergata'')

created by gelli on 09 Nov 2015

modified on 11 Nov 2015

25 nov 2015 -- 17:00

Aula Seminari Dipartimento di Matematica di Pisa

**Abstract.**

The notion of minimizing movement (Almgren-Taylor-Wang, De Giorgi),
which has been used to give a general definition of gradient flow
(Ambrosio-Gigli-SavarÃ©)
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.