Lecture

Variational Problems: Quasi-Convexity

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In course

MATH-604: Some Aspects of Calculus of Variations

The goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals. ...

Description

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.

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