Geodesic
On the Poincar\'e Inequality for Periodic Composite Structures
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 261 (2008), pp. 301-303.

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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. 
@article{TM_2008_261_a23,
     author = {V. V. Shumilova},
     title = {On the {Poincar\'e} {Inequality} for {Periodic} {Composite} {Structures}},
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V. V. Shumilova. On the Poincar\'e Inequality for Periodic Composite Structures. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 261 (2008), pp. 301-303. http://geodesic.mathdoc.fr/item/TM_2008_261_a23/

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