Homogenization of a variational problem in three-dimension space

摘要

In this paper, we investigate the variational problem for a sequence of 3-dimensional domains with highly oscillating boundaries. Using the unfolding method and the averaging method, we obtain the result of the homogenization problem, that is, a sequence of solutions of Eq. (3.1) converges to the solution of Eq. (3.4) as the periodic length approaches zero. It is noteworthy that the convergence is in the strong sense.