# 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

- Due October 23, 9:15 a.m.
pdf or html
- Due October 30, 9:15 a.m. pdf or html
- Due November 6, 9:15 a.m. pdf or html
- Due November 13, 9:15 a.m. pdf or html
- Due November 20, 9:15 a.m. pdf or html
- Due October 27, 9:15 a.m. pdf or html
- Due December 4, 9:15 a.m. pdf or html
- Due December 11, 9:15 a.m. pdf or html
- Due December 18, 9:15 a.m. pdf or html
- Due January 8, 9:15 a.m. pdf or html
- Due January 15, 9:15 a.m.
pdf or html
- 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