Lecture
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05 Nov 2021 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Introduction to Geometric Measure Theory, basic properties of Lipschitz functions
12 Nov 2021 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Covering theorems and differentiation of measures
19 Nov 2021 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Hausdorff measures
27 Nov 2021 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Rectifiable sets, k-dimensional Jacobians, Area formula
03 Dic 2021 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Proof of the area formula. Preliminaries on the proof of the coarea formula
10 Dic 2021 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Role of negligible sets in the coarea formula and rectifiability of level sets. Signed and vector valued measures: compactness, continuiity and lower semicontinuity results
17 Dic 2021 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Rectifiability criteria for measures, approximate tangent space, disintegration. Introduction to Young measures.
14 Gen 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Fundamental compactness properties of Young measures, convex functions and their recession.
21 Gen 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Proof of joint lower semicontinuity. Reshetnyak's continuity and lower semicontinuity theorems. Introduction to sets of finite perimeter.
29 Gen 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Equivalence of distributional and variational definitions of BV and sets of finite perimeter. BV functions and sets of finite perimeter in one variable.
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