MRI course 'Variational and Topological Methods for Nonlinear Partial Differential Equations'

Lecturers: Jan Bouwe van den Berg and Mark Peletier
Course dates: each Wednesday, 10.15-13, in 276 BBL
Background material: L. C. Evans, Partial Differential Equations

Course history and plan:

• 4/2 (Van den Berg): Introduction, Brouwer's fixed point theorem, Banach fixed point theorem, application to ODEs and nonlinear PDEs. Exercises: 9.7.3-4.
• 11/2 (Peletier): Linear parabolic theory: weak solutions, H^{-1}, fundamental estimate (E: 5.9.1, 7.1.1, 7.1.2b). Exercises: 9.7.3 (again)
• 18/2 (Peletier): CANCELLED
• 25/2 (Peletier): Schauder fixed point theorem (E: 9.2.2), and exercises
• 4/3 (Peletier): Schauder fixed-point theorem II (see e.g. the version in this wikipedia article) and Schäfer's fixed-point theorem (E 9.2.2); exercises
• 11/3 (Peletier): short test over all context discussed up to and including 4/3
• 18/3 : CANCELLED
• 25/3 (Van den Berg): Variational methods: convexity, Euler-Lagrange equation for unconstrained minimization, examples; Exercises
• 1/4 (Peletier) weak topologies; Exercises
• 8/4 (Van den Berg): short test;
• 15/4 (Peletier): existence of minimizers for general integrands L (Evans 8.2); Exercises
• 22/4 (Van den Berg): Exercises
• 29/4 (Van den Berg): short test;
• 6/5 (Van den Berg): non-minimizer critical points, Mountain pass lemma, examples; exercises
• 13/5 (Van den Berg): exercises
• 20/5 (Peletier):
• 27/5 (Van den Berg): final exam