Webrelaunch 2020

Variationsmethoden (Winter Semester 2022/23)

Lecture: Tuesday 9:45-11:15 20.30 SR 2.67
Wednesday 9:45-11:15 20.30 SR 2.67
Problem class: Thursday 14:00-15:30 20.30 SR 3.68
Lecturer, Problem classes Prof. Dr. Tobias Lamm
Office hours:
Room 2.040 Kollegiengebäude Mathematik (20.30)
Email: tobias.lamm@kit.edu
Problem classes Dr. Gianmichele Di Matteo
Office hours:
Room 2.035 Kollegiengebäude Mathematik (20.30)
Email: g.dimatteo@kit.edu

In order to attend the exam, please send an e-mail to g.dimatteo@kit.edu .

The following list of PDF files covers the material seen in the exercise classes.

Functional Analysis Preliminary Brezis H., "Functional Analysis, Sobolev Spaces and Partial Differential Equations", Springer, 2011
Plateau's problem Struwe M., "Variational Methods", Springer, 2007
Concentration-Compactness Principle Lions P.L., "The concentration-compactness principle in the calculus of variations. The locally compact case, part 1", Ann. Inst. H. Poincar´e Anal. Non Lin´eaire, 1984
Radon Measures Maggi F., "Sets of Finite Perimeter and Geometric Variational Problems", CUP, 2012
Independence of the critical Sobolev's constant from the domain Struwe M., Calculus of Variation notes 2019
Best constant in Sobolev's inequality Talenti G., "Best constant in Sobolev inequality", Ann. Mat. Pura Appl., 1976
Functions of Bounded Variation Evans L.C., Gariepy R.F., "Measure Theory and Fine Properties of Functions", CRC Press, 2015
"Direct method" of the CoV for the Perimeter Maggi F., "Sets of Finite Perimeter and Geometric Variational Problems", CUP, 2012
Differentiability of Nemitski's Operators Ambrosetti A., Prodi G., "A primer of Nonlinear Analysis", CUP, 1993
Struwe M., Tarantello G. - On multivortex solutions in Chern-Simons gauge theory Boll. Unione Mat. Ital. Vol. 1-B, Issue 1, 1998, (see pages 119-120)
Volume functional Struwe M., "Variational Methods", Springer, 2007
Alexandrov's moving plane method Ros A., "The isoperimetric problem"