Explores the Legendre transform, duality in convex analysis, and optimization problems.
Explores the classical methods for solving optimization problems, emphasizing the Euler-Lagrange equation and its variants.
Covers the Euler-Lagrange equation in Sobolev spaces and discusses minimization, convexity, and weak forms.
Explores polyconvexity in vectorial calculus with open bounded sets and Lipschitz boundaries, weak continuity theorems, and function space minimization.
Explores regularity in 1D functions, emphasizing weak derivatives and minimizers.
Explores regularity in higher dimensions for scalar problems and discusses weak sense solutions and interior regularity.
