Nichtlineare Randwertprobleme/Nonlinear boundary value problems (Winter Semester 2010/11)
- Lecturer: Prof. Dr. Michael Plum
- Classes: Lecture (1054), Problem class (1055)
- Weekly hours: 4+2
Prof. Dr. Michael Plum / Dipl.-Math. techn. Rainer Mandel
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 in-vestigated 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.
| Schedule | ||
|---|---|---|
| Lecture: | Monday 11:30-13:00 | 1C-01 |
| Friday 9:45-11:15 | Z 1 | |
| Problem class: | Wednesday 15:45-17:15 | 1C-01 |
| Lecturers | ||
|---|---|---|
| Lecturer, Problem classes | Prof. Dr. Michael Plum | |
| Office hours: Please get in contact by email. | ||
| Room 3.028 Kollegiengebäude Mathematik (20.30) | ||
| Email: michael.plum@kit.edu | Problem classes | PD Dr. Rainer Mandel |
| Office hours: by appointment | ||
| Room -1.019 Kollegiengebäude Mathematik (20.30) | ||
| Email: rainer.mandel@kit.edu | ||