Homogenization of elasticity problems on singular structures

We consider homogenization theory on periodic networks, junctions and more general singular objects. We show that the homogenized problem typically has a “non-classical” character. This fact is a distinctive feature of homogenization of elasticity problems in contrast to scalar problems.
We investigate the properties of Sobolev spaces for various singular structures, prove a non-classical homogenization principle for singular periodic structures of general type and describe a “scaling effect” for model problems with two small geometrical parameters.