Variational Problems: Convexity and Coercivity

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.