Advanced Partial Differential Equations,
Ort und Termin
|Lecture (VO) 3 hrs.||9:45-11:15
|Proseminar 1 hr.
Approximation in Lp and mollification [Teschl, Section 10.4]. Sobolev spaces [Teschl, Section 13.1], [Evans, Chapter 5]. To be continued....
The following problems should be prepared:
- Problem Set 1 (due 11.10): [Teschl] 10.18, 10.19, 10.21, 10.23
- Problem Set 2 (due 18.10): [Teschl] 10.24, 13.1, 13.2, 13.4
- Problem Set 3 (due 25.10): [Teschl] 13.6, 13.7, 13.8 [Evans] 5.10 Problem 3
- Problem Set 4 (due 8.11): [Evans] 5.10 Problem 4, 7, 8 (Instructions for 4: The absolutely continuous functions are the antiderivatives of integrable functions (see Theorem 11.49 in my notes). Now have a look at the hint for Problem 14.19 in my notes.)
- Problem Set 5 (due 15.11): [Teschl] 13.10, 13.13
- Problem Set 5 (due 22.11): [Teschl] 13.14 [Evans] 5.10 Problem 20, 21 Please download the latest version of the notes!
The topics covered during class will be documented here.
Module "Advanced Partial Differential Equations" in the Master's programme in Mathematics
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.
- H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011.
- L.C. Evans, Partial Differential Equations, 2nd ed., Amer. Mat. Soc., 2010.
- D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 2001.
- G. Grubb, Distributions and Operators, Springer, New York, 2009.
- G. Teschl, Topics in Real and Functional Analysis, Amer. Math. Soc., Providence, to appear.