*Information about the course*

**January to May, 2017, Wednesday / Thursday, 14:30 – 16:00, room 2122, building 9: **

I am giving a course on **Weak Solutions of PDE**** (AMCS 232)**. This will be a *hard* and *difficult* course.

The course begins with an introduction to distributions and weak derivatives. Next, we consider Sobolev spaces and fundamental results: extension and trace theorems, Poincare’s inequality and Rellich-Kondrachov theorem. Then, we examine weak solutions of elliptic equations through Lax-Milgram theorem.

A substantial part of the course will involve the students presenting individually some of the lecture material and papers.

**Please get a copy** of the book *Partial Differential Equations* by L. C. Evans. **You will need it** on Wednesday, January 31st.

*Schedule of the presentations*

Sections of the book *Partial Differential Equations *assigned / to be assigned:

**Week 1:**

5.2 – 5.2.2: A. A.

5.2.2 – 5.2.3: W. A.

**Week 2:**

5.2.3 – 5.3: R. C.

5.3 – 5.3.3: M. S.

**Week 3:**

5.3.3 – 5.4 Theorem 1 proof: F. A.

5.4 Theorem 1 proof – 5.5: M. K.

5.5 – 5.6: G. S.

**TBA:**

5.6 – 5.6 Theorem 2

5.6 Theorem 2 – 5.6.2 Theorem 5

5.6.2 Theorem 5 – 5.7

**Instructions for the presentations**

**Instructions for the presentations**

- 30 minutes per presentation
- understand the material you are going to present
- if you have questions, google them, ask other students in the class
- ask yourself: is the notation clear? are all definitions clear? what does the theorem mean? what questions could be asked?
- present the theorems and the main ideas of the proof
- only use the whiteboard; you can put information you will refer to repeatedly on a few slides, e.g. you can put a theorem on a slide and refer to it while presenting the proof on the whiteboard. Bring your own laptop if you use slides.
- use your own hand-written notes
- practice your presentation

**Office hours **

**Office hours**

Please make an appointment by email at least 48 hours before

**Feedback**

**Feedback**

Students can leave anonymous feedback and suggestions for improvements on this google form.

*Useful Links*

- Multi-index
- General Leibniz rule
- $L^p$-spaces
- Step functions dense in $L^p$
- Translation continuous in $L^p$