MAP5, Université Paris Descartes and IUFM Paris

email:

**Abstract**: We study periodic reiterated homogenization for
equations of the form
, where
is a Carathéodory function. Under appropriate growth and
monotonicity assumptions and if the sequence of reiterated unfolding converges
almost everywhere to a Carathéodory type function, the sequence of solutions
converges to the solution of a limit variational problem. In particular this
contains the case
, where is
periodic in the second and third arguments, and continuous in each argument.

We also study the homogenization in the monotone multivalued case for equations of the form , with , where is a function whose values are maximal monotone.