Syllabus
1. Real-analytic properties of Sobolev functions
Riesz potential estimate
Beppo Levi's characterization
Embedding theorems
Approximate differentiability, a.e. differentiability
Examples concerning discontinuity and non-differentiability 2. Change of variables in integral for Lipschitz transforms
Area formula
Coarea formula
Sard type theorems
Luzin's (N) condition 3. Differentiation of convex functions
Lipschitz estimates
Zajíček's theorem (informatively)
Alexandrov's theorem
Annotation
Real-analytic properties of Sobolev functions. Change of variables in integral for Lipschitz transformations – area and coarea formula.
Differentiation of convex functions. Recommended for master students of mathematical analysis.