Cornell Math - MATH 620, Spring 2000

MATH 620 — Spring 2000
Partial Differential Equations

We will cover a fundamental portion of the theory of partial differential equations, which is central to much of modern differential geometry and applied mathematics.

Core Content

Sobolev and Holder spaces; embedding theorems; Rellich-Kondrachov compactness theorem; existence and regularity theory for elliptic second order equations.

Further Topics

Calculus of variations — the direct method; basic parabolic theory analogous to the elliptic theory above.

Advanced Topics (if time permits)

Harmonic maps or other nonlinear PDE theory.

Depending on the backgrounds of the audience, we will insert some more basic theory concerning maximum principles, and perhaps some prerequisite functional analysis.