Institut für Angewandte Mathematik
Lecture in the summer term 2020
Calculus of variations
Lecturer
Content
  • Dirichlet principle
  • Variation, Gateaux and Frechet derivative
  • Euler-Lagrange equations
  • Convex variational problems, monotone operators
  • Weak lower semi-continuity, generalized Weierstrass existence theorem
  • Nonlinear eigenvalue problems
  • Nonlinear operator equations in Banach spaces
  • Applications
Lecture and practical
Exercise sheets
Literature
  • E. Zeidler, Applied Functional Analysis, Applied Mathematical Sciences Vol. 108, Springer, 1995.
  • E. Zeidler, Applied Functional Analysis, Applied Mathematical Sciences Vol. 109, Springer, 1995.
  • M. Růžička, Nichtlineare Funktionalanalysis, Springer, 2004.
  • B. Dacorogna. Direct Methods in the Calculus of Variations. 2nd ed. Springer, 2008.
  • I. Ekeland, R. Temam. Convex analysis and variational problems. Elsevier, 1976.
  • P. Blanchard, E. Brüning. Direkte Methoden der Variationsrechnung, Springer-Verlag Wien New York, 1982.
Lecture notes by Prof. Jussi Behrndt (in German) can be found here.
Notes of last lecture can be found here.