Lecture 6
II. Basics of GMT (Hausdorff measure, Hausdorff dimension, Rectifiable sets, purely unrectifiable sets)
Lecture 5
II. Oscillation (revisiting the proof of the two phase problem). II. Linear PDE Constrained Measures. The rank-one theorem, the De Philippis—Rindler theorem and a first idea of proof, Tangent measures (strict convergence, non-triviality).
Lecture 3
II.2 Oscillation. Motivation in nonlinear PDEs and Calculus of Variations. Two phase oscillations with a PDE constraint (pure, approximate).
Lecture 2
Recap of Basic Geometric Measure Theory: measures, integration, outer measures, Lp spaces, weak convergence, Riesz’ representation theore, compactness in Lp and spaces of measures
Lecture 1
Introduction: Motivation and some examples. Setting of linear PDE systems with constant coefficients.