Variational homogenization: old and new
Rita Ferreira
King Abdullah University of Science and Technology (KAUST), CEMSE Division, Thuwal 23955-6900, Saudi ArabiaIrene Fonseca
Department of Mathematical Sciences, Carnegie Mellon University(CMU), Forbes Avenue, Pittsburgh, PA 15213, USARaghavendra Venkatraman
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA
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Abstract
This note is a summary of the contributions of the authors to the variational viewpoint on homogenization. After providing a broad context, two recent projects are discussed in detail: one concerning the large-scale behavior of quasicrystals, and the other involving phase transitions in periodically heterogeneous media.