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Arbeitsgruppe Nichtlineare Partielle Differentialgleichungen

Kollegiengebäude Mathematik (20.30)
Zimmer 3.029

Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe



Analysis I, II, III: für Studierende der Mathematik, Lehramt Mathematik, Physik, Informatik, Ingenieurpädagogik, Schülerstudenten

HM I, II: für Studierende der Informatik

sowie studienbegleitende Klausuren zu den Vorlesungen der Dozenten der Arbeitsgruppe.

Mo-Fr: 10-12, Di+Mi: 14-16

Tel.: 0721 608 42064

Fax.: 0721 608 46530

Nonlinear boundary value problems (Wintersemester 2016/17)

Dozent: Prof. Dr. Michael Plum
Veranstaltungen: Vorlesung (0104600), Übung (0104605)
Semesterwochenstunden: 4+2

Vorlesung: Dienstag 15:45-17:15 SR 3.68
Freitag 11:30-13:00 SR 3.68
Übung: Mittwoch 15:45-17:15 SR 3.68
Dozent Prof. Dr. Michael Plum
Sprechstunde: Fr 13:15 - 14:15 und nach Vereinbarung
Zimmer 3.028 Kollegiengebäude Mathematik (20.30)
Email: michael.plum@kit.edu
Übungsleiter Dr. Peter Rupp
Sprechstunde: montags 14:00-15:00Uhr oder nach Vereinbahrung
Zimmer 3.026 Kollegiengebäude Mathematik (20.30)
Email: peter.rupp@kit.edu


The lecture course will be concerned with boundary value problems for nonlinear
elliptic partial differential equations, mainly of second order. In contrast to the linear
case, no "unified" existence theory is at hand, but various approaches for proving
existence (and other properties) of solutions need to be studied. The methods investigated
in the lecture course are subdivided into non-variational and variational
A preliminary and incomplete list of topics:
- Motivating examples
- monotonicity methods
- fixed-point methods
- super- and subsolutions
- non-existence results
- radial symmetry
- a short introduction into variational calculus
- Euler-Lagrange equations
- variational problems under constraints
- critical points
- mountain pass theorem
- perturbation results


Knowledge in functional analysis (Hilbert- and Banach spaces, weak convergence,
dual space, Frechet differentiable operators) is essential, as well as the Lebesgue
integral and Sobolev spaces. Knowledge in the classical theory of partial differential
equations, and about weak solutions to linear problems, will be very useful.


Will be given in the first week of the semester.

Exercise Sheets

Exercise sheet 1
Exercise sheet 2
Exercise sheet 3
Exercise sheet 4
Exercise sheet 5
Exercise sheet 6
Exercise sheet 7
Exercise sheet 8
Exercise sheet 9
Exercise sheet 10
Exercise sheet 11
Exercise sheet 12
Exercise sheet 13
Exercise sheet 14