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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

Mo-Fr 10:00-12:00, sowie Di+Do nachmittags

Tel.: 0721 608 42064

Fax.: 0721 608 46530

Nichtlineare Randwertprobleme/Nonlinear boundary value problems (Wintersemester 2010/11)

Dozent: Prof. Dr. Michael Plum
Veranstaltungen: Vorlesung (1054), Übung (1055)
Semesterwochenstunden: 4+2

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.

Vorlesung: Montag 11:30-13:00 1C-01
Freitag 9:45-11:15 Z 1
Übung: Mittwoch 15:45-17:15 1C-01
Dozent, Übungsleiter Prof. Dr. Michael Plum
Sprechstunde: Do 13:30 - 14:30 und nach Vereinbarung
Zimmer 3.028 Kollegiengebäude Mathematik (20.30)
Email: michael.plum@kit.edu
Übungsleiter Dr. Rainer Mandel
Sprechstunde: Nach Vereinbarung
Zimmer -1.019 Kollegiengebäude Mathematik (20.30)
Email: rainer.mandel@kit.edu