Variationsmethoden (Winter Semester 2022/23)
- Lecturer: Prof. Dr. Tobias Lamm, Dr. Gianmichele Di Matteo
- Classes: Lecture (0105450), Problem class (0105460)
- Weekly hours: 4+2
| Schedule | ||
|---|---|---|
| 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 |
| Lecturers | ||
|---|---|---|
| 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"
Weak lower semicontinuity, Giusti E., "Direct Methods in the Calculus of Variations", World Sci. Pub., 2005
Bolza-Young's example Muller S., "Variational models for microstructure and phase transitions", Lecture C.I.M.E., 1996
Dacorogna-Marcellini's example Dacorogna B., Marcellini P., "A counterexample in the vectorial calculus of variations", 1988
Mania`'s example Ferriero A., "The Lavrentiev phenomenon in the Calculus of Variations", 2004
Sverak's example of rank-one convex but non quasi-convex Muller S., "Variational models for microstructure and phase transitions", Lecture C.I.M.E., 1996
Sverak's example of quasi-convex but non poly-convex function Sverak V., "Quasiconvex functions with subquadratic growth", Proc. R. Soc. Lond. A, 1991