MATH-604 / 3 credits
Teacher: Radici Emanuela
Remark: Fall semester - Tuesdays 2 - 4pm - online. Exam session on Thursday January 14th from 9h15 to 13h15 by ZOOM
Only this year
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.
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, and the main assumptions that allows for a solid existence and regularity theory of such vector-valued problems. If the time allows, we will also cover some aspects of variational convergence of functionals (Γ convergence).
Direct method, Euler Lagrange equations, lowersemicontinuity, convexity
Basic courses of analysis and Functional analysis
By the end of the course, the student must be able to:
- understand when it is possible to apply and how to use the Direct method of calculus of variations, describe the eventual osbtacles and how to overcome them
In the programs
- Exam form: Oral presentation (session free)
- Subject examined: Some Aspects of Calculus of Variations
- Lecture: 28 Hour(s)
- Practical work: 28 Hour(s)