Lecture plan
The lecture plan will be continuously updated.
| Date | Topics |
|---|---|
| Calculus of variations and PDEs | |
| Week 3 | Introduction and examples Dirichlet integral and Laplace equation Weak and strong Euler-Lagrange equation Weak derivatives The Sobolev space \(H^1\) Weak and strong Euler-Lagrange equation |
| Week 4 | Variational methods for image processing Weak solutions of PDEs Relation to Galerkin methods PDEs as operator equations in Hilbert spaces Lax–Milgram theorem |
| Week 5 | Application of Lax–Milgram to variational problems Optimality conditions for simple optimal control problems Carathéodory functions Monotone, coercive, and hemi-continuous operators Browder–Minty theorem |