# MA8105 Ikkelineære partielle differensialligninger og Sobolevrom

**Lecturer:** Helge Holden Email: holden [at] math [dot] ntnu [dot] no

**Textbook:** H. Holden: "Tools from the Toolbox. Functional Analysis for Partial Differential Equations" (notes will handed out to the students taking the course).

**Time for Lectures:** (the lectures will be in English)

- Thursday at 10:15-12:00 in room 922, Sentralbygg 2
- Friday at 08:15-10:00 in room 734, Sentralbygg 2

**Lecture plan:**

- Fri, Jan. 9: p. 5-9. Exercises 2-4 (p. 33) strongly recommended.
- Thu, Jan. 15: p. 10-14.
- Fri, Jan. 16: NO lecture.
- Thu, Jan. 22: p. 15-17.
- Fri, Jan. 23: CHANGE of lecture time: 8:15-12:00 (8-10 in room 734, 10-12 in room 922), p. 19-25.
- Thu, Jan. 29: p. 17-19, 35-37.
- Fri, Jan. 30: p. 38-42.
- Thu, Feb. 5: p. 42-44.
- Fri, Feb. 6: p. 44-48.
- Thu, Feb. 12: p. 49-53.
- Fri, Feb. 13: p. 54-58.
- Thu, Feb. 19: p. 50-62.
- Fri, Feb. 20: p. 63-68. The proof of Dunford-Pettis was skipped. You are all urged to do Example 4.22 (p. 68) in all details.
- Thu, Feb. 26: p. 69-71
- Fri, Feb. 27: p. 72, 83-87
- Thu, March 5: p. 93-97
- Fri, March 6: p. 97-99
- Thu, March 12: NO lecture
- Fri, March 13: CHANGE of lecture time: 8:15-12:00 (8-10 in room 734, 10-12 in room 922), p. 99-105.
- Thu, March 19: NO lecture
- Fri, March 20: CHANGE of lecture time: 8:15-12:00 (8-10 in room 734, 10-12 in room 738), p. 105-109.
- Thu, March 26: p. 109-111
- Fri, March 27: p. 112, Pages from Larsson and Thomee: "Partial Differential Equations with Numerical Methods", p. 51-55. Exercise: Show equations (5.7) and (5.8).
- Thu, April 9: p. 53-55 from Larsson & Thomee, and exercises (equations (5.7) and (5.8)). More exercises
- Fri, April 10: We will do the exercises. P. 76-80 on Young measures
- Thu, April 16: NO lecture
- Fri, April 17: More on Young measures

**Exam:** The exam is oral. At the day of the exam you meet at 9:00 am in my office. The time for each candidate will be decided then.

**Curriculum:** pages 1-25, 35-72 (not proof of Thm. 4.15), 76-83 (no proofs), 83-87, 93-113, the notes from Larsson and Thomee.

**Regulations concerning the exam**:
For the first 20 min the candidate presents a lecture using blackboard only on one of the topics given below. Notes are allowed. It should be a lecture presenting the main parts of the topic, or if the topic is big, a selected part of it. Proofs are encouraged. After that, and for approximately 25 min the candidate will be asked questions about all of the curriculum. Here there will of course be no notes. The topic is decided at the beginning of the exam.

**Topics:** (A) Sections 2.1-2.2; (B) Ch. 3; (C) Sections 4.1-4.4; (D) Sections 5.1-5.3; (E) Sections 5.4-5.7; (F) Notes by Larsson and Thomee.