Direct method in the calculus of variations

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Calculus of Variations: Gradient Young Theorem

Covers the Gradient Young Theorem in the calculus of variations, discussing proofs and applications.

Calculus of Variations and Euler's Elastica

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.

Calculus of Variations: Radon-Nikodym Theorem

Covers the Radon-Nikodym theorem and the uniqueness of signed Borel measures.

Blow up Technique

Explores the Blow up Technique in Variations, emphasizing its role in establishing boundedness and verifying integral fractional properties.

Variations: Jensen-Type Inequality

Covers the Jensen-Type inequality for young meanres and the connection between young and quasi convexity.

Calculus of Variations and Euler's Elastica

Explores the calculus of variations and Euler's Elastica in the context of beam equilibrium and inextensible elastic curves under large rotations.

Euler-Lagrange Equation

Explores the classical methods for solving optimization problems, emphasizing the Euler-Lagrange equation and its variants.

Optimal Control Theory: Basics

Covers the fundamentals of optimal control theory, focusing on defining OCPs, existence of solutions, performance criteria, physical constraints, and the principle of optimality.

Variational Calculus: Quasicovexity

Explores quasicovexity in variational calculus, discussing necessary conditions and implications on functional optimization.

Calculus of Variations: Principles and Applications

Explores the principles and applications of calculus of variations, focusing on uniform boundedness and equi-integrability of Carathéodory integrands.