Multi-parameter homogenization by localization and blow-up

Felipe Alvarez, Jean-Philippe Mandallena
2004 Proceedings of the Royal Society of Edinburgh. Section A Mathematics  
It is given an alternative self-contained proof of the homogenization theorem for periodic multiparameter integrals that was established by the authors in [4] . The proof in that paper relies on the so-called compactness method for Γ-convergence while the one presented here is by direct verification: the candidate to be the limit homogenized functional is first exhibited, the definition of Γ-convergence is then verified. This is done by extension of bounded gradient sequences using the Acerbi
more » ... using the Acerbi et al. extension theorem from connected sets [2] , and by adaptation of some localization and blow-up techniques developed by Fonseca and Müller [14] together with De Giorgi's slicing method [11] .
doi:10.1017/s0308210500003498 fatcat:luhoocmp3zbm7nwqtyhbsrge6a