Characterization of two-scale gradient Young measures and application to homogenization

Jean-François Babadjian (1) , Margarida Baia (2) , Pedro M. Santos (2)

1 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
2 IST - Instituto Superior Técnico, Universidade Técnica de Lisboa

This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures.

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Babadjian, Margarida Baia, Pedro M. Santos. Characterization of two-scale gradient Young measures and application to homogenization. Applied Mathematics and Optimization, 2008, 57 (1), pp.69-97. ⟨10.1007/s00245-007-9012-y⟩. ⟨hal-00265692⟩