Nonlinear boundary value problems (Wintersemester 2016/17)
- Dozent*in: Prof. Dr. i.R. Michael Plum
- Veranstaltungen: Vorlesung (0104600), Übung (0104605)
- Semesterwochenstunden: 4+2
| Termine | ||
|---|---|---|
| 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 |
| Lehrende | ||
|---|---|---|
| Dozent | Prof. Dr. i.R. Michael Plum | |
| Sprechstunde: Kontakt via E-Mail. | ||
| 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 | ||
Contents
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
methods.
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
Prerequisites
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.
References
Will be given in the first week of the semester.