Partial Differential Equations 1, winter 2021/2022
Course taught by Sebastian Schwarzacher.
Materials
The lectures will (mostly) follow the lecture notes (Czech-English version) by M. Bulíček, M. Pokorný & others.
Homeworks
There will be weekly homework assignments. You can hand in your solutions preferably on the Wednesday lecture, alternatively you can send them by email.
Course overview
| Week | Lecture | chapters in lecture notes | Homework |
|---|---|---|---|
| 1 | Lebesgue spaces, Smoothing, Eigenvalue problem for Laplace equation notes |
A.3.2-A.3.5, section 2.2 of this |
HW 1: Laplace equation deadline: 6.10.2021 11:30 |
| 2 | Hölder spaces, Gauss theorem, weak derivative and Sobolev spaces |
HW 2: Classical, weak and distributional derivatives deadline: 13.10.2021 11:30 |
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| 3 | HW 3: Sobolev spaces deadline: 20.10.2021 11:30 |
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| 4 | HW 4: Dual of Lp spaces deadline: 27.10.2021 11:30 |
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| 5 | HW 5: Euler-Lagrange equation deadline: 3.11.2021 11:30 |
6 | HW 6: Linear elliptic PDE deadline: 10.11.2021 11:30 |
| 7 | HW 7: Sobolev embeddings deadline: 24.11.2021 11:30 |
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| 8 | HW 8: Poincaré inequalities deadline: 1.12.2021 11:30 |
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| 9 | HW 9: Regularity deadline: 8.12.2021 11:30 |
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| 10 | HW 10: Regularity II deadline: 15.12.2021 11:30 |
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| 11 | 14.12.2021 - lecture recording 15.12.2021 - lecture recording |
HW 11: Linear parabolic equations deadline: 22.12.2021 11:30 |
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| 12 | 21.12.2021 - lecture recording 22.12.2021 - lecture recording |
HW 12: Linear parabolic equations II deadline: 5.1.2022 11:30 |