Increase of dimension by homogenization

The paper deals with the homogenization of a Neumann's problem in a thin pe riodic "weakly connected" domain of R-3. The domain Omega (n) is composed o f a large number n of disjoint periodic connected components linked by a pe riodic lattice omega (n) of very thin bridges. According to the distributio n 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 ad ditional term corresponding to the increase of dimension is due to the conn ection effect of the bridges.