Classical Methods for Partial Differential Equations (Winter Semester 2021/22)
- Lecturer: Prof. Dr. Tobias Lamm
- Classes: Lecture (0105300), Problem class (0105310)
- Weekly hours: 4+2
Anyone interested in reviewing the corrections of the exam dated 21/02/22 should send an e-mail to g.dimatteo@kit.edu before the end of this week.
Registration for the exam of the 11^th of April 2022 are now open. The results of the exam dated 21/02/22 are now online. If you want to see the scripts again, send an e-mail to g.dimatteo@kit.edu before the end of this week.
| Schedule | ||
|---|---|---|
| Lecture: | Tuesday 10:00-11:30 | 20.30 1. OG R. 1.66/ 1.67 |
| Thursday 10:00-11:30 | 20.30 1. OG R. 1.66/ 1.67 | |
| Problem class: | Wednesday 14:00-15:30 | 10.91 Redt. |
| Lecturers | ||
|---|---|---|
| Lecturer, Problem classes | Prof. Dr. Tobias Lamm | |
| Office hours: | ||
| Room 2.040 Kollegiengebäude Mathematik (20.30) | ||
| Email: tobias.lamm@kit.edu | Problem classes | Dr. Gianmichele Di Matteo |
| Office hours: | ||
| Room 2.035 Kollegiengebäude Mathematik (20.30) | ||
| Email: g.dimatteo@kit.edu | ||
In this introductory lecture to the theory of Partial Differential Equations we start by studying the three model equations:
- the Laplace equation
- the heat equation
- the wave equation
in a classical setting. Once this is done we show the existence and regularity of weak solutions of more general elliptic PDE's in Sobolev spaces.
Basics on Hölder spaces
Exercise Sheets
Exercise sheet 1
Solutions to sheet 1
Exercise sheet 2
Exercise sheet 3
Exercise sheet 4
Exercise sheet 5
Exercise sheet 6
Exercise sheet 7
Exercise sheet 8
Solutions to sheet 8
Exercise sheet 9
Log is BMO
Some exercises
Exercise sheet 10
Exercise sheet 11
Exercise sheet 12
Some exercise for the exam preparation- NEW VERSION WITH SOLUTIONS
exam 21/02/22 solutions
References
- Evans, L.C.: Partial Differential Equations
- Giaquinta, M. / Martinazzi, L.: An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs
- Gilbarg, D. / Trudinger, N.: Elliptic Partial Differential Equations of second order
- Han, Q.: A basic course in Partial Differential Equations
- Han, Q. / Lin, F.: Elliptic Partial Differential Equations
- Jost, J.: Partial Differential Equations