Advanced Topics in Analysis (2023)

Updates:

2023/05/15: The page is published.
2023/05/16: Typos in LectNote03.pdf and LectNote04.pdf are corrected.
- Eq. (2.5) in LectNote03.pdf; eq. (2.13) in LectNote04.pdf
- I think (I hope) I wrote them correctly on the blackboard.
- Thank you to the student who pointed out this👍
2023/05/19: Typos in Problem 3 is corrected.
- In the hint, the norm is the $L^2$-norm $\| \cdot \|$ and not the $H^1$-norm $\| \cdot \|_{H^1}$.
2023/05/22:
- Added a reference.
- Added Problem 4 and Problem 5.
- Added a comment on the blow-up of $\| u(t) \|_{L^{\infty}}$ in finite time.

Lecture notes: