Deterministic homogenization of non-linear non-monotone degenerate elliptic operators

Deterministic homogenization has been till now applied to the study of monotone operators, the determination of the limiting problem being systematically based on the monotonicity of the operator under consideration. Here we mean to show that deterministic homogenization also tackle non-monotone operators. More precisely, under an abstract general hypothesis, we study the homogenization of non-linear non-monotone degenerate elliptic operators. We obtain some general homogenization result, which result is applied to the resolution of several concrete homogenization problems such as the periodic homogenization and the almost periodic homogenization problems. Our main tool is the theory of homogenization structures.