V5B5 - Advanced Topics in Analysis and Calculus of Variations: Regularity for Elliptic Variational Problems
Instructor:
Dr. Franz Gmeineder
Timetable:
Exam (oral):
Course Synopsis:
Prerequisites:
- Analysis 1–3 and Functional Analysis. An introductory course on partial differential equations is helpful, but not mandatory. Students that took the course 'Nonlinear PDE 1' from winter term 2018/19 will discover some overlaps, but this course is essentially self-contained.
Specific course material:
- Lecture Notes (Updated Thu, May 9)
- L. Ambrosio, N. Fusco, D. Pallara: Functions of bounded variation and free discontinuity problems. Oxford University Press, 2000.
- L. Beck: Elliptic Regularity Theory - A first course. Lecture Notes of the Italian Mathematical Union, Springer, 2016.
- E. Giusti: Direct Methods in the Calculus of Variations. World Scientific, 2003.
- G. Mingione: Regularity of minima: an invitation to the dark side of the calculus of variations. Appl. Math. 51 (2006), no. 4, 355–426.
- A more extensive list of relevant background material is available here.
- Lecture notes will be available and shall be updated weekly.
Background Reading:
News
The Mathematical Institute mourns Günter Harder
Floris van Doorn and coauthors receive the Skolem Award
Hausdorff Center for Mathematics receives 7 additional years of funding
Markus Hausmann receives Minkwoski medal of the DMV
Rajula Srivastava receives Maryam Mirzakhani New Frontiers Prize
Dennis Gaitsgory receives Breakthrough Prize in Mathematics 2025
Daniel Huybrechts elected as member of Leopoldina
Catharina Stroppel appointed Honorary Doctor at Uppsala University
Angkana Rüland receives Gottfried Wilhelm Leibniz Prize 2025
Wolfgang Lück receives the von Staudt Prize
Gerd Faltings elected member of the Order Pour le Mérite
Geordie Williamson receives the Max Planck-Humboldt Research Award 2024