Deterministic homogenization on problems of minimal hypersurface type

We study here the deterministic homogenization for a particular family of convex integral functionals, namely problems of minimal hypersurfaces. By the sigma-convergence method relooked especially in appropriate representation of non-periodic functions and in the extension of sigma-convergence on the L1L1-space, we obtain a general homogenization result, and thanks to the particularity of minimal hypersurfaces, we derive a macroscopic integral functional. We then provide a number of physical applications (including the periodic case) of this result.