Topics of Advanced Analysis

General characterization

Prerequisites

Available soon

Bibliography

Bibliography on Calculus of Variations
- B. Dacorogna, Direct methods in the calculus of variations. Second edition. Applied Mathematical Sciences, 78. Springer, New York, 2008.
- B. Dacorogna, Introduction to the Calculus Variations,Third edition, Imperial College Pork, 2008.ress, London, 2015.
- I. Fonseca, G. Leoni, Modern methods in the calculus of variations: Lp spaces, Springer Monographs in Mathematics, Springer, New York, 2007.
- F. Rindler, Calculus of variations, Universitext, Springer, Cham, 2018.

Teaching method

During the lectures the problems and appropriate methods to treat them are introduced. Most results are proven. A list of exercises is provided to be solved by the students.

All questions are discussed either during the classes or in other sessions with this purpose.

Evaluation method

The evaluation is a mark between 0 and 20 values and the student passes if the final mark is above or equal to 9,5.

1) the resolution and handing over of a list of exercises (corresponding to 35% of the final mark);
2) the study and presentation of a book chapter (corresponding to 30% of the final mark);
3) the study and presentation of a paper within the scope of the subject (corresponding to 35% of the final mark);

Subject matter

Introduction: problems of the calculus of variations and its mathematical formulation. Examples.

Classical methods: Euler-Lagrange equation, Hamiltonian system, Hamilton-Jacobi equation.

Direct method: sequential weak lower semi-continuity, convexity, quasiconvexity, polyconvexity, and rank-1 convexity.

Developments in the calculus of variations: relaxation, differential inclusions, gamma-convergence.

Programs

Programs where the course is taught: