Fiches de cours

Some Aspects of Calculus of Variations

MATH-604

Lecturer(s) :

Radici Emanuela

Language:

English

Frequency

Only this year

Remarque

Next time: Fall 2019

Summary

The goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals

Content

The aim of this course is to give an introduction to the classical and modern calculus of variations with a focus on the theory of integral functionals defined on spaces of vector-valued maps in several variables. This is due to the fact that many physical, technological and economical systems incorporate some kind of variational principle, and the understanding of this structure is essential to obtain meaningful results about them. We will discuss topics as the Direct Method in Calculus of Variations, the lower semicontinuity, convexity, polyconvexity, quasiconvexity and relaxation of the functionals for the existence and the regularity of solutions of the vector-valued problems. If the time allows, we will also cover some aspects of variational convergence of functionals (¿ convergence).

Keywords

Direct method, quasiconvexity, polyconvexity, relaxation

Learning Prerequisites

Required courses

Basic courses of analysis and Functional analysis

Learning Outcomes

By the end of the course, the student must be able to:

In the programs

  • Mathematics (edoc), 2019-2020
    • Semester
    • Exam form
      Oral presentation
    • Credits
      3
    • Subject examined
      Some Aspects of Calculus of Variations
    • Lecture
      28 Hour(s)
    • Practical work
      28 Hour(s)

Reference week

Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German