Title: Homogenization of nonlinear elliptic systems in nonreflexive Musielak-Orlicz spaces,
Abstract: We study the homogenization process for families of strongly nonlinear
elliptic systems with the homogeneous Dirichlet boundary conditions. The growth
and the coercivity of the elliptic operator is assumed to be indicated by a
general inhomogeneous anisotropic $N-$function, which may be possibly also
dependent on the spatial variable, i.e., the homogenization process will change
the characteristic function spaces at each step. Such a problem is well known
and there exists many positive results for the function satisfying $\Delta_2$
and $\nabla_2$ conditions an being in addition Hölder continuous with
respect to the spatial variable. We shall show that cases these conditions can
be neglected and will deal with a rather general problem in general function
space setting.