MA8105 Distribusjonsteori og Sobolevrom med anvendelser

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).

Lectures: (the lectures will be in English)

  • Tuesday 12:15-14:00, room 922, Sentralbygg 2
  • Thursday 10:15-12:00, room 822, Sentralbygg 2

Plan for lectures:

  • Tue, Jan 18: pages 5-7
  • Thu, Jan 20: pages 8-10
  • Tue, Jan 25: no lecture
  • Thu, Jan 27: pages 11-15
  • Tue, Feb 1: no lecture, but homework: Sec 2.1 up to Thm 2.21
  • Thu, Feb 3: Lemma 2.17, pages 18-19
  • Tue, Feb 8: pages 21-23 (incl sec. 2.2)
  • Thu, Feb 10: Ch. 3, p. 35-36, homework up to Prop. 3.4
  • Tue, Feb 15: Ch. 3, p. 39 (Prop. 3.4)-42
  • Thu, Feb 17: The remaining part of Ch. 3.
  • Mon, Feb 21 (observe date!) : Sec. 4.1-2. Room 922 at 10:15-12.
  • Tue, Feb 22: no lecture
  • Thu, Feb 24: no lecture
  • Mon, Feb 28 (observe date and time!) : Sec. 4.3-4. Room 922 at 8:15-10.
  • Tue, March 1: Sec. 4.4.
  • Thu, March 3: Sec. 4.5.
  • Tue, March 8: Sec. 4.4.
  • Thu, March 10: Sec. 4.5.
  • Tue, March 15: Sec. 4.6.
  • Thu, March 17: Young measures.
  • Mon, March 21: Smooth approximations. Room 922 at 8:15-10.
  • Tue, March 22: no lecture
  • Thu, March 24: Smooth approximations, Bochner spaces.
  • Mon, March 28: Sobolev spaces. Room 922 at 8:15-10.
  • Tue, March 29: no lecture
  • Thu, March 31: Extensions.
  • Tue, April 5: Traces.
  • Thu, April 7: Estimates.
  • Tue, April 12: Compactness.
  • Thu, April 14: Compactness.

Exam: The exam is oral. Date: Monday, June 6, 2011. All candidates are requested to meet at 1156 SII at 9:15.The order of the candidates will then be decided. Curriculum: Ch.1: all; Ch. 2: sections 2.1, 2.2; Ch. 3: all; Ch. 4: all; Ch. 5: all.

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 4.1-4.3, 4.8; (D) Sections 4.4-4.7; (E) Sections 5.1-5.3; (F) Sections 5.4-5.8;

2011-04-29, Helge Holden