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Lecture course: Partial differential equations II

Tu, Th 10 - 12 in B 251


Organisation of tutorials: Ingo Wagner       You will find the problem sheets here

NEWS

  • 26.07.10   You can pick up certificates and graded exams in Mrs Warcholik's office.

  • 20.07.10   Textbook references to Chapter 3 on operator semigroups have been added to the script after page 97.

  • 23.06.10   Pages 65 and 66 have been updated with 2 corrections: growth exponent in Assumption (A2) changed to p-1. This ensures validity of the integrability estimate in Part (i) of the proof of Thm. 2.19 even for Sobolev functions η (previously only for smooth functions).

  • 09.06.10   Script updated; note that the set A on top of p. 46 needs to be not only convex but also closed.

  • 25.05.10   There will not be a tutorial on Th, 27 May. Instead this tutorial will take place on Tu, 1 June 10 at 10:15 in B 251 (instead of the lecture – as announced previously).

  • 06.05.10   Problem Sheet 3 suffered from 2 typos, which have been corrected now.

  • 06.05.10   Two changes in schedule: (1) On Th, 20 May 2010 the lecture will take place from 8:30 to 10:00 in B 040, while the tutorial will start at 10:15 in B 251.
    (2) On Tu, 1 June 10 there will be a tutorial at 10:15 in B 251 instead of the lecture.

  • 06.5.10   The script has been updated. Please note the modified assumptions on aij, bj, c on p. 21 (just above Def. 1.24).

Synopsis
This is a continuation of the course Partial differential equations, which I gave in the winter term 09/10. We will continue with the weak theory of solutions for second-order linear equations, study the variational approach to PDE's and discuss more specific methods like ones based on fixed-point theorems.

Prerequisites
Partial differential equations (if you have not attended this course, you should have at least some background in the theory of Sobolev spaces)

Audience
Students of Mathematics (Bachelor, Diploma, Lehramt), Financial Mathematics (Diploma), Physics (Bachelor, Diploma), Elite-Master Course Theoretical and Mathematical Physics (TMP)

Literature
See part I of the course

Contents (as pdf with page numbers)
  1. Linear evolution equations

    1.1.  Analytic tools   (pdf)
    1.2.  Time-dependent Sobolev spaces   (pdf)
    1.3.  Weak theory of parabolic equations   (pdf)
    1.4.  Weak theory of hyperbolic equations   (pdf)

  2. Calculus of variations   (pdf)

    2.1.  One-dimensional variational problems   (pdf)
    2.2.  Multi-dimensional variational problems   (pdf)
    2.3.  Minimisation under constraints   (pdf)
    2.4.  Existence of stationary points   (pdf)

  3. Operator semigroups   (pdf)


(I am happy to receive feedback on misprints, etc., in order to improve future updates)