Calculus of Variations and Geometric Measure Theory

G. Bouchitté - G. Buttazzo - I. Fragalà

Bounds for the effective coefficients of homogenized low dimensional structures

created on 06 Jun 2001
modified on 10 Dec 2003


Published Paper

Inserted: 6 jun 2001
Last Updated: 10 dec 2003

Journal: J. Math. Pures Appl.
Volume: 81
Number: 5
Pages: 453-469
Year: 2002


For a given amount $m$ of mass, we study the class of materials which can be reached by homogenization distributing the mass $m$ on periodic structures of prescribed dimension $k\leq n$ in $\ren$. Both in the scalar case of conductivity and in the vector-valued case of elasticity, we find some bounds for the effective coefficients, depending on the mass $m$ and the dimension parameters $k, n$. In the scalar case we prove that such bounds are optimal, as they do describe the set of all materials reachable by homogenization of structures of the type under consideration; in the vector-valued case we show that some of our estimates are attained.