Calculus of Variations and Geometric Measure Theory

A. Braides - V. Chiadò Piat

Non convex homogenization problems for singular structures

created by braidesa on 16 Jun 2007
modified on 08 Jul 2008


Published Paper

Inserted: 16 jun 2007
Last Updated: 8 jul 2008

Journal: Netw. Heterog. Media
Volume: 3
Number: 3
Pages: 489 - 508
Year: 2008


We prove a homogenization theorem for non-convex functionals depending on vector-valued functions, defined on Sobolev spaces with respect to oscillating measures. The proof combines the use of the localization methods of $\Gamma$-convergence with a `discretization' argument, which allows to link the oscillating energies to functionals defined on a single Lebesgue space, and to state the hypothesis of $p$-connectedness of the underlying periodic measure in a handy way.

Keywords: Homogenization, Singular structures, p-connectedness