Course info

Course Contents
Classical treatment of the fundamental types (e.g. elliptic, parabolic, hyperbolic, dispersive), formulation of elliptic boundary value problems as variational problems, regularity theory, theory of Sobolev spaces, Galerkin methods, fixed point methods and nonlinear elliptic and parabolic equations

Literature
L.C. Evans: Partial Differential Equations (AMS)
D. Gilbarg, N.S. Trudinger: Elliptic Partial Differential Equations of Second Order (Springer)
W. Ziemer: Weakly Differential Functions (Springer)

Preconditions
recommended: Functional Analysis

Official Course Description
This is supposed to be a first advanced course in Partial Differential. Equations (PDEs). We will treat these equations from a modern point of view, using in particular a new definition of derivatives (weak derviatives) that will allow us to use Hilbert space techniques for differentiable functions. Many of the results in this course will be showcases for general phenomena and results in the field of PDEs.

Online Offerings
Moodle