Lecture
Euler-Lagrange Equation
Description
This lecture covers the classical methods for solving optimization problems, focusing on the Euler-Lagrange equation. It explains the concept of stationary points and the variants of the equation with different boundary conditions and constraints. The instructor discusses the existence of solutions, convexity, and regularity issues, emphasizing the importance of studying the solutions to understand the minimization process. The fundamental lemma of the calculus of variations is introduced, along with practical examples and applications in ODEs and PDEs.
Official source
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