Admissible functions in two-scale convergence. (English) Zbl 0886.35018

Valadier, Michel

Port. Math. 54, No. 2, 147-164 (1997).

Summary: The two-scale convergence method was developed by G. Nguetseng, W. E and G. Allaire in connection with homogenization problems. We introduce a rather large class of “admissible” functions containing Carathéodory integrands of both kinds (continuous on \(\Omega\) or on \(Y\)) and prove a useful continuity result. Through all the paper we use the notion, introduced by W. E, of “two-scale” Young measures. This also provides natural proofs of some quantitative results of Huygens type.

MSC:

35B27	Homogenization in context of PDEs; PDEs in media with periodic structure
28A20	Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
35B40	Asymptotic behavior of solutions to PDEs
49J45	Methods involving semicontinuity and convergence; relaxation

Keywords:

oscillations; Young measures; results of Huygens type