Periodic Reiterated Homogenization of Monotone Operator

Nicolas Meunier
MAP5, Université Paris Descartes and IUFM Paris
email: meunier@ann.jussieu.fr

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.