Advanced Partial Differential Equations,
Winter 2017

Place and Time
Type: Time: Place: Start:
Lecture (VO) 3 hrs. 9:45-11:15
13:30-14:14
HS02
SR11
3.10.
Proseminar 1 hr.
12:30-13:15 SR11 4.10.
About
This course gives an introduction to the functional analytic treatment of partial differential equations.
Proseminar
The following problems should be prepared:
Content
Approximation in Lp and mollification [Teschl, Section 10.4]. Sobolev spaces [Teschl, Chapter 13], [Evans, Section 5.1-5.8]. Second-order elliptic PDE [Evans, Section 6.1-6.3.1]. Operator semigroups [Teschl, Chapter 7], [Evans, Section 7.4]. Calculus of Variations [Evans, Sections 8.1.1-8.1.3] To be continued....
Target audience
Module "Advanced Partial Differential Equations" in the Master's programme in Mathematics
Assessment
The course assessment for the lecture (VO) will be via an oral examination at the end of the course. The course assessment for the introductory seminar (PS) will be via participation (solving/presenting assigned problems) during the seminar.
Literature

Some textbooks

  1. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011.
  2. L.C. Evans, Partial Differential Equations, 2nd ed., Amer. Mat. Soc., 2010.
  3. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 2001.
  4. G. Grubb, Distributions and Operators, Springer, New York, 2009.
  5. G. Teschl, Topics in Real and Functional Analysis, Amer. Math. Soc., Providence, to appear.
Looking forward to seeing you, Gerald Teschl