Geodesic
Homogenization of elasticity problems on singular structures
Izvestiya. Mathematics , Tome 66 (2002) no. 2, pp. 299-365

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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. 
@article{IM2_2002_66_2_a2,
     author = {V. V. Zhikov},
     title = {Homogenization of elasticity problems on singular structures},
     journal = {Izvestiya. Mathematics },
     pages = {299--365},
     publisher = {mathdoc},
     volume = {66},
     number = {2},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_2_a2/}
}
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V. V. Zhikov. Homogenization of elasticity problems on singular structures. Izvestiya. Mathematics , Tome 66 (2002) no. 2, pp. 299-365. http://geodesic.mathdoc.fr/item/IM2_2002_66_2_a2/