Increase of Dimension by Homogenization

The paper deals with the homogenization of a Neumann's problem in a thin periodic weakly connected domain of R ³. The domain _n is composed of a large number n of disjoint periodic connected components linked by a periodic lattice _n of very thin bridges. According to the distribution and to the size of the linking bridges, the limit problem as n tends to infinity is either a 4d Neumann's problem or a 4d nonlocal problem. The additional term corresponding to the increase of dimension is due to the connection effect of the bridges.