Young measure minimizers in the asymptotic analysis of thin films

Abstract

An integral representation for a relaxed functional arising in the membrane theory is obtained in terms of Young measures generated by sequences ${( abla_{alpha}u_{varepsilon_n } ig| frac{1}{varepsilon_n } abla _3 u_{varepsilon_n})} $ of scaled gradients.

Keywords

• Equi-integrability
• concentrations
• oscillations
• relaxation
• Young measure.