Vorlesung: Partielle Differentialgleichungen II (PDG2) (SoSe 2020)
[UPDATE 06.04.2020:] Due to the present situation, this course will be online (uploaded videos, lecture notes, homework exercises). It may move to the class room if the situation improves.
It will start 21 April 2020 (as planned).
For updated information, check back here, on LSF, and on uni2work (where all material will be uploaded).
A brief video introduction can be found here.
Hence, some of the information below (time schedule, office hours) is, at present, obsolete.
Lecture (Vorlesung):
Tue 14--16 (in B 132) & Wed 10--12 (in B 134). First time (Erstes Mal): 21 April 2020.
Exercises (Ãœbungen):
See separate webpage (uni2work). LSF
Tutorials (Tutorien):
There are NO tutorials!
Synopsis (Kurzbeschreibung):
This lecture is a continuation of the introductory lecture 'Partielle Differentialgleichungen' (PDG1) in the past semester (WiSe2019/20).
It can also be taken as a continuation of any other introductory lecture 'Partielle Differentialgleichungen' (PDG1).
We will study existence and regularity of weak solutions to elliptic equations. This will also involve the study of weak derivatives and Sobolev spaces (on domains).
Audience (Hörerkreis):
Master students of Mathematics (WP 40), Master students of `Finanz- und Versicherungsmathematik' (WP 27), TMP-Master.
Credits:
9 (6+3) ECTS.
Prerequisites (Vorkenntnisse):
Analysis I–III, Linear Algebra I–II, Functional Analysis, PDE1 (in some form; approximately p. 1–90 in [E] Evans (see below)).
Language (Sprache):
English. (Die mündliche Prüfung kan auch auf Deutsch gemacht werden).
Exam (Prüfung):
There will be an oral exam (dates to be announced) (Es wird eine mündliche Prüfung geben).
See separate webpage (uni2work).
Content (Inhalt):
- Introduction and motivation
- Weak derivatives & Sobolev spaces
- Linear 2nd order elliptic PDE
- Nonlinear elliptic equations
- Evolution equations & C_0 - semigroups
In uni2work you will find a copy of the notes from the lecture (to be updated as we go along).
Above you will find a short description of the content of the lecture (to be updated as we go along).
The lecture will mainly follow the books by Evans, and Arendt & Urban mentioned below.
- [E] L. C. Evans, Partial Differential Equations: Second Edition, AMS, Providence, RI, 2010. (NOT available online!)
- [A-U] W. Arendt, K. Urban, Partielle Differenzialgleichungen, Springer Spektrum, 2018. (Login with your Campus-account.)
- H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011.
- V. Maz'ya, Sobolev spaces, with Applications to Elliptic Partial Differential Equations, Springer, 2011.
- D. D. Haroske, H. Triebel, Distributions, Sobolev Spaces, Elliptic Equations, EMS, 2007.
- G. Grubb, Distributions and Operators, Springer, 2009.
- R. Precup, Linear and Semilinear Partial Differential Equations, De Gruyter, 2013.
- G. Leoni, A First Course in Sobolev Spaces: Second Edition, AMS, 2017.
Office hours (Sprechstunde):
Thursday 10.15-11.00 (Room B 408) or by appointment via email.
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Letzte Änderung: 03 September 2020 (No more updates)
Thomas Østergaard Sørensen