Second Level Degree in Mathematics
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CALCULUS OF VARIATIONS - 8 CFU
Teacher
Roberto Monti
Scheduled Period
I Year - 2 Semester | 02/03/2020 - 12/06/2020
Hours: 64 (32 esercitazione, 32 lezione)
Prerequisites
The Analysis 1 and 2 and the Real Analysis courses
Target skills and knowledge
The classical formalism of the calculus of variations in its hystorical development, with applications and motivations to geometry and physics. The development of the modern theory of the calculus of variations in the setting of Sobolev spaces.
Examination methods
Homeworks and oral exam
Assessment criteria
The teacher will ascertain the student's proficiency in the course's main subjects
Course contents
Introduction to the classical formalism of the Calculus of Variations: indirect methods, first variation, Euler-Lagrange equations, applications.
First direct methods, working in spaces of Lipschitz functions, via a priori gradient estimates.
Modern direct methods: introduction to Sobolev spaces and their use in minimization problems. Tonelli's theorem and the XX problem of Hilbert.
Introduction to currents.
Introduction to optimal transportation
Plateau problem
Planned learning activities and teaching methods
Blackboard lessons
Additional notes about suggested reading
The reference material will be communicated during the course.