Calculus of Variations

Functionals and their derivative play an essential role in the many applications, e.g., differential equations (and other equations on mathematical physics) can sometimes be written as critical point (vanishing derivative) of a functional. Often the solution of such an equation is equivalent to the minimization of a corresponding functional. The course will explore this relation. Basic concepts to be treated will be: derivatives (variations) of functionals of infinite dimension (typically function spaces), convexity, weak topology, the Banach-Alaoglu theorem, weak semi-continuity, minimax principles, and Sobolev spaces. The applications will include examples from physics (Poisson equation, Thomas-Fermi equation and others) as well as applications from geometry (minimal surface equations) and numerics.

Exercise sheets

  1. Due October 23, 9:15 a.m. pdf or html
  2. Due October 30, 9:15 a.m. pdf or html
  3. Due November 6, 9:15 a.m. pdf or html
  4. Due November 13, 9:15 a.m. pdf or html
  5. Due November 20, 9:15 a.m. pdf or html
  6. Due October 27, 9:15 a.m. pdf or html
  7. Due December 4, 9:15 a.m. pdf or html
  8. Due December 11, 9:15 a.m. pdf or html
  9. Due December 18, 9:15 a.m. pdf or html
  10. Due January 8, 9:15 a.m. pdf or html
  11. Due January 15, 9:15 a.m. pdf or html
  12. Due January 22, 9:15 a.m. pdf or html

The course will take place Tuesdays from 2:15 p.m to 4 p.m. and Fridays from 9:15 p.m. to 11 p.m. in room E 46. There will be exercises on Tuesday from 11:15 a.m. to 1 p.m. in room 252 be in room E 46.

Heinz Siedentop