• Espen R. Jakobsen

• email: erj@math.ntnu.no

• Office hours: Monday 16:15-17:00

• Monday 14:15-16:00 in B23 (Berg)

• Friday 10:15-12:00 in S21 (SB2)

• Plan/log, see 'Lectures' in the left menu.

• Weekly exercises, see "Execises" in the left menu.

• Hints, partial solutions, or references in Appendix C in the lecture note.

• Problem session: Friday 9:15-10:00, room 656 SB2 (student run)

• Holden: Tools from the toolbox. Functional Analysis for Partial Differential Equations.
• You will get the note at the first lecture.

Not part of the curriculum.

• Brezis: Functional Analysis, Sobolev Spaces, and Partial Differential Equations, Springer 2011. (Chapters 1, 3, 4, 8, 9 are relevant)
  
  
• Ciarlet: Linear and Nonlinear Functional Analaysis with Applications, SIAM 2013.
  
  
• Evans: Partial Differential Equations, AMS 2010. (Chapter 5 on Sobolev spaces)
  
  
• Gilbarg and Trudinger: Elliptic Partial Differential Equations of Second Order, Springer 1998. (Chapter 7 on Sobolev spaces)
  
  
• Holden, Risebro: Front Tracking for Hyperbolic Conservation Laws, Springer 2015. (Appendix A on compactness, chapter 3 on finite difference methods)
  
  
• Vazquez: The Porous Medium Equation, Oxford 2007.
  
  
• Folland: Real Analysis, Wiley 1999. (Chapter 7 on Radon measures)

• From Holden Tools from the toolbox: sections 1, 2.1, 3, 4.1-4.5, 4.7, 5.1-5.5, 5.7, 7 (Theorem 7.1 with proof), Appendix A (except Theorem A2 and A3), Appendix B.

• Handwritten notes by Espen on Porous Medium Equations.

• All homework problems.

• Oral

• The exam has two parts:
  
  
  1. (20 min): One of the topics given below is randomly selected and the candidate then gives a presentation of it on the blackboard (no slides).
     Focus on the main parts of the topic, or if the topic is big, a selected part of it. Proofs are encouraged.
     
     Notes are allowed - but watch the time - 20 min.
     
     
  2. (25 min): Examination in all of the curriculum. No notes.

• Topics (from Tools from the toolbox):
  
  (A) Sections 2.1; (B) Chapter 3; (C) Sections 4.1-4.3; (D) Sections 4.4-4.5, 4.7; (E) Sections 5.1-5.3; (F) Sections 5.4-5.6, 5.7.

• Dates: