Calculus of Variations (WiSe 20/21)
Lectures (first one on January 5th): Tuesday, 8-10, and Wednesday, 12-14 (the videos of the lectures are uploaded on Lecture2Go).
Exercise classes (first one on January 5th): Tuesday, 16-18 (in this BigBlueButton room).
Assistant: Anton Treinov.
Office hours: Please write me an email to email@example.com in order to set up a meeting on BigBlueButton.
Modular structure and ECTS points: The lecture is a 6-ECTS module over the second half of the term.
Prerequisites: The lecture builds on basic knowledge in analysis (including the theory of Lebesgue integration) and linear algebra, and some familiarity with either PDEs or advanced analysis is recommended. Brief reminders on functional analysis and Sobolev spaces may be given here and there, but in principle the participants are assumed to have or acquire some basic knowledge on these topics.
Calculus of variations in Sobolev spaces (key topics: direct method, semicontinuity and existence, Euler-Lagrange equations).
Lecture notes: Calculus of Variations (WiSe 19/20) - Prof. T. Schmidt.
Lawrence C. Evans, Partial Differential Equations, American Mathematical Society, 1998.
Mariano Giaquinta, Luca Martinazzi, An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs, Edizioni della Normale, 2012.
Enrico Giusti, Direct Methods in the Calculus of Variations, World Scientific, 2003.
The exercise sheet will be uploaded on STiNE every Tuesday by 10:00.
Instead of handing in the solutions weekly, every student has to present the solutions of one exercise sheet via BigBlueButton
to the other participants. The presentation does not have to be a LaTeX pdf, it is sufficient to share your scanned or photographed readable handwritten notes
and explain your solutions step by step.