Homogenization of nonlinear monotone operators beyond the periodic setting

Abstract

We study the homogenization of nonlinear monotone operators beyond the classical periodic setting. The usual periodicity hypothesis is here replaced by an abstract assumption covering a wide range of concrete behaviours such as the periodicity, the almost periodicity, the convergence at infinity, and many more besides. Our approach is based on the recent theory of homogenization structures by the first author. The exactness of the results confirms the major role the homogenization structures are destined to play in a general deterministic homogenization theory equipped to consider the physical problems in their true perspective.