Mathematics Behind Microstructures: A Lead to Generalizations of Convexity

  • Daniel Vasiliu
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 24)


We consider a mathematical model aimed at explaining pattern formation in microstructures. Usually such models are also useful for understanding problems of solid–solid phase transitions in material science. Our goal is to analyze the limiting behavior of certain non-linear energy type functionals, with restrictions, from a variational point of view. In order to better understand this problem we develop some generalizations for the notions of rank-one convexity and quasi-convexity and demonstrate their relevance in the context of energy minimizing sequences.


Microstructures Rank-one convexity Quasiconvexity Restricted lower semicontinuity 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of MathematicsChristopher Newport UniversityNewport NewsUSA

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