Calculus of Variations
Winter 2022/23
Content of the lecture
The first part of the lecture is dedicated to the direct method of variational calculus. This method is usually used to show existence of solutions of partial differential equations.
We will also work out the functional analytic background, needed to employ this method.
The second part of the lecture will concentrate on a so called Mountain-Pass Lemma, which is useful in showing non-uniqueness of solutions of PDEs.
Oral exams
The oral exams will take place on
23rd of February,
31st of March or
12th of April.
Please send me your prefered date till the 18th of January together with your complete name and matriculation number.
Lecture notes
The lecture notes can be found here.
These notes are freshly typed, so please expect typos and other small errors. I will update the lecture notes during the semester.
Exercises
Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6
Solutions
Solution of sheet 1
Solution of sheet 2
Solution of sheet 3
Solution of sheet 4
Solution of sheet 5
Solution of sheet 6
Requirements
Analysis 1-4, Linear Algebra 1
An introduction to partial differential equations or functional analysis is useful, but not required.
Literature
- Michael Struwe: Variational Methods, Springer 2008, fourth edition.
- David Gilbarg, Neil S. Trudinger: Elliptic partial differential equations of second order. Springer 1998.
- Walter Rudin: Functional Analysis, Mc Graw Hill Education 1991, second edition.
Additional Informations
Lecturer: Dr. Sascha Eichmann, Link
Time of the Lecture: Wednesdays, 14-16
Room Lecture: C5H10 rsp. S07
Time of the Exercise class: Tuesdays every two weeks, 08-10.
Room Exercise class: C5H10 rsp. S07
Language: English or german, depending on the students preference
ECTS-Points: 5
Announcement: Since the 1st of November is a holiday, the exercise class in this week will be on Friday the 4th of November, 16-18, in S07.
Impressum