First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP3050978, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2019/20
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination CALCULUS OF VARIATIONS
Website of the academic structure
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge ROBERTO MONTI MAT/05

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/05 Mathematical Analysis 8.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 4.0 32 68.0 No turn
Lecture 4.0 32 68.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2011 course timetable

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 unit 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.
Textbooks (and optional supplementary readings)