Variational Problems: Quasi-Convexity

This lecture covers the theory of quasi-convexity in the context of variational problems originating from continuum mechanics. The instructor explains the concepts of weakly coercive functionals, quasi-convexity, and the Direct Method of Calculus of Variations. The lecture delves into the physical interpretation of quasi-convexity and provides examples to illustrate the principles. It also discusses the relationship between quasi-convexity and convexity, showcasing counterexamples to highlight the differences. The presentation concludes with a detailed proof and the application of quasi-convexity in solving variational problems.