Calculus of variations

MATH-437

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Course summary

Teacher: Dr. Alexis Michelat
Assistant: Jaime Gómez Ramírez

Lectures

The lectures of the course will be held in person every Friday morning from 8:15am to 10:00am in the room MA B1 11.

Lecture notes will be updated every week and uploaded after the lecture at the following link.

Exercise Sessions
The exercise session will take place on Friday morning between 10:15am and 12:00am (in the same room MA B1 11).

Schedule

LECTURE ROOM

Lectures: Friday, 8.15 – 10.00, MA B1 11
Exercises: Friday, 10.15 – 12.00, MA B1 11

Course content   

Introduction to classical Calculus of Variations and a selection of modern techniques. The Calculus of Variations aims at showing the existence of minimisers (or critical points) of functionals that naturally appear in mathematics and physics (Dirichlet energy, p-energy, etc). We will have to introduce basic notions on distribution theory, Sobolev space, and spend some time discussing notions of convexity in the calculus of variations. In the last part of the course, we will treat the problem of Plateau, that consists in solving a problem of the calculus of variations where convexity does not hold (the problem is about finding the surface of least area amongst all surfaces of prescribed boundary).

Exam


The exam will take place on the 19th of June 2025 (Thursday) from 08:15 to 18:15 (in MA A1 12)


Your individual schedule will be communicated in June.


The exam is an oral exam divided into two parts.  First, the exam is given (the candidate will be able to choose one exercise amongst many) and the examinee has 30 minutes to prepare. After this delay, the oral exam starts and lasts for 30 minutes.


No documents are allowed.


In terms of length and difficulty, the exercises will be comparable to the first two exercises from the exam below :