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Nichtlineare Randwertprobleme/Nonlinear boundary value problems (Winter Semester 2010/11)

Prof. Dr. Michael Plum / Dipl.-Math. techn. Rainer Mandel

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

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.

Lecture: Monday 11:30-13:00 1C-01
Friday 9:45-11:15 Z 1
Problem class: Wednesday 15:45-17:15 1C-01
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