Mathematical Institute of the University of Bonn

V3B1 - Functional Analysis and Partial Differential Equations

Instructor: Prof. Dr. Herbert Koch
Assistant: Dr. Franz Gmeineder

Timetable:

Wednesdays, 10 am (c.t.) - 12am, Wegelerstraße 10, Kleiner Hörsaal
Fridays, 8 am(c.t.) - 10 am, Wegelerstraße 10, Kleiner Hörsaal

Exam:

• The final exam for the course takes place on Saturday, Feb 15, 2020, from 9-11 am. If you are taking the exam within the Bachelor program, please come to the 'Kleiner Hörsaal' (Wegelerstraße 10), if within the Master program, please come to the 'Großer Hörsaal' (Wegelerstraße 10). You will be allowed to enter the respective lecture theaters at 8:45 am; thus, please arrive at Wegelerstraße 10 early enough.

Course Synopsis:

The course intends to give an introduction to linear functional analysis and its applications in partial differential equations.

Prerequisites:

• Analysis 1–3 and Linear Algebra 1,2. Introduction to PDEs (EPDG) is helpful but not mandatory.

Revision Class:

We offer monthly revision classes for the course, in which we give a review of the concepts encountered so far and attempt sample problems. The first class takes place on Friday, Nov 22, 2019, in Wegelerstraße 10, Kleiner Hörsaal (!) from 4(ct)-6pm. If you have specific questions you would like to have covered in class, please send an e-mail to F. Gmeineder (fgmeined(famousletter)math.uni-bonn.de).

The second revision class takes place on Fri, Dec 06, 2019, 4(st)-5:30 in the Zeichensaal (Wegelerstraße 10).

Tutorial Sessions:

• There will be weekly tutorial sessions (starting from term week 2). The slots shall be assigned during the first lecture (Oct, 09).

Time	Venue	Tutor
Mondays, 8-10 am	SemR 0.008	Sascha Horstmann
Mondays, 10-12 am	SemR 0.008	Sebastian Schmidt
Tuesdays, 4-6 pm	SemR 0.008	Linus Behn
Thursdays, 8-10 am	SemR 0.008	Frederick Wehr

Problem Sets:

Here you find the weekly problem sets; please staple your solutions.

• Problem Set 1 (Due: Oct 18, 2019)
• Problem Set 2 (Due: Oct 25, 2019)
• Problem Set 3 (Due: Nov 07, 2019)
• Problem Set 4 (Due: Nov 15, 2019)
• Problem Set 5 (Due: Nov 22, 2019)
• Problem Set 6 (Due: Nov 29, 2019)
• Problem Set 7 (Due: Dec 06, 2019); in Ex. 2 replace f_j by f.
• Problem Set 8 (Due: Dec 13, 2019)
• Problem Set 9 (Due: Dec 20, 2019)
• Problem Set 10 (Due: Jan 10, 2020)
• Problem Set 11 (Due: Jan 17, 2020)
• Problem Set 12 (Due: Jan 24, 2020)
• Very easy additional exercises (not quite...)


Background Reading:
• Lecture notes (as of Feb, 02)
• E. Stein & R. Shakarchi: Functional Analysis. Princeton University Press, 2012.
• G. Allan: Introduction to Banach Spaces and Algebras. Oxford University Press, 2010. <\li>
• P. Lax: Functional Analysis. Wiley Interscience, 2002.
• K. Yosida: Functional Analysis. Springer Classics in Mathematics, 1996.
• E. Lieb, M. Loss: Analysis. AMS Graduate Studies in Mathematics, 2001.
• D. Werner: Funktionalanalysis. Springer, 2012.
• H.-W. Alt: Lineare Funktionalanalysis. Springer, 2008.
• W. Kaballo: Funktionalanalysis. Spektrum, 2011.
• M. Dobrowolski: Funktionalanalysis. Springer Masterclass, 2009.
• G. Mingione: Regularity of minima: an invitation to the dark side of the calculus of variations. Appl. Math. 51 (2006), no. 4, 355–426.