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Lecture

Variational Problems: Convexity and Coercivity

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 fundamental concepts of variational problems, focusing on convexity and coercivity conditions. The instructor explains the theorems related to these topics, illustrating how to determine minimizers for functionals with integral side constraints. The lecture delves into the Electrostatics example to demonstrate the application of these theorems. The discussion extends to the Tarelli-Serrin theorem and weakly-loc properties of functions. The lecture concludes by exploring the Laurentian Gap Phenomenon and the challenges it poses for numerical approximation in optimization problems.

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