Topic Course: Geometric Measures and Conservation Laws
Hilary Term 2020,
Prof.
Gui-Qiang G. Chen
Duration: 8 hours
Overview:
This is a graduate lecture
course as an introduction to some facets of geometric measures and conservation
laws, and related applications. Basic Analysis and PDE are the only essential
prerequisites. However, some familiarity with basic measure theory, functional
analysis, nonlinear PDEs , and differential geometry
is desirable.
Topics:
1. Connections: Geometric Measures and
Conservation Laws
2. Review: Basic Measure Theory
3. Hausdorff Measures
4. Area/Co-Area Formulas
5. BV Functions and Sets of Finite Perimeter
6. Theory of Divergence-Measure Fields and
Connections with
7. Conservation Laws
8. *Differentiability and Approximation
9. *Varifolds and
Currents
10. *Further Connections with Nonlinear PDEs
*Optional
Lecture Notes:
Lecture 0
Lecture 1
Lecture 2
Lecture
3
Lecture 7*