On the Poincaré Inequality for Periodic Composite Structures

We consider periodic composite structures characterized by a periodic Borel measure equal to the sum of at least two periodic measures. For such a composite structure, verifying the Poincaré inequality may be a difficult problem. Thus, we are interested in finding conditions under which it suffices to verify the Poincaré inequality separately for each of the simpler structure components instead of verifying it for the composite structure.