Geodesic
On the compactness principle in variable space $L^p$ for periodic composite structures
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 526-532

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We consider the compactness principle in the variable space $L^p$ related to a periodic Borel measure. It is supposed that the periodic Borel measure describes a periodic singular or composite structure. We prove the compactness principle for periodic grids, box structures, involving Cantor's constructions, and corresponding composite structures.
Keywords: periodic structures, periodic Borel measure, compactness principle. 
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     author = {V. V. Shumilova},
     title = {On the compactness principle in variable space $L^p$ for periodic composite structures},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {526--532},
     publisher = {mathdoc},
     volume = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2009_6_a24/}
}
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V. V. Shumilova. On the compactness principle in variable space $L^p$ for periodic composite structures. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 526-532. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a24/