Advanced Partial Differential Equations,
Winter 2021
Place and Time
| Type: | Time: | Place: | Start: |
| Lecture (VO) 3 hrs. | Mon: 8:00-8:45 Thu 8:00-9:30 |
HS02 HS13 |
4.10. |
| Proseminar 1 hr. |
Fri 11:30-12:15 | SR10 | 8.10. |
News
We had to switch to online. Please see the Moodle course.
About
This course gives an introduction to the functional analytic treatment of partial differential equations.
Proseminar
The following problems should be prepared:
- 8.10: 1,2,3,4,5
- 15.10: 6,7,8,9
- 15.10: 10,11,12,13
- 29.10: 14,15,16,17
- 5.11: 18,19,20,21
- 12.11: 22,23,24,25
- 19.11: 26,27,28,29
- 26.11: 30,31,32,33
- 3.12: 34,35,36,37
- 10.12: 38,39,40,41
- 17.12: 42,43,44,45
- 7.1: 46,47,48,49
- 14.1: 50,51,52,53
- 21.1: 54,55,56,57
- 28.1: 58,59,60,61
Content
I will assume familiarity with Lebesgue spaces and basic Functional Analysis.
We covered the second part of my notes [PDE]
except for Sections 14.3 and 14.4.
Target audience
Module "Advanced Partial Differential Equations" in the Master's programme in Mathematics
Assessment
The course assessment for the lecture (VO) will be via an oral examination at the end of
the course. The course assessment for the introductory seminar (PS) will be via
participation (solving/presenting assigned problems) during the seminar.
Literature
Some textbooks
- H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011.
- L.C. Evans, Partial Differential Equations, 2nd ed., Amer. Mat. Soc., 2010.
- D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 2001.
- G. Grubb, Distributions and Operators, Springer, New York, 2009.
- G. Teschl, Topics in Real and Functional Analysis, Amer. Math. Soc., Providence, to appear.
- G. Teschl, Partial Differential Equations, Lecture notes.