Lecture
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04 Feb 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Proof of the Fleming-Rishel coarea formula, monotone and BV functions, calibrations, examples of local minimizers
11 Feb 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Poincare' and isopetrimetric inequalities, in local and global form. Localization lemma and definitions of measure-theoretic boundaries
18 Feb 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Proof of the structure theorem of sets of finite perimeter. Fine properties of BV functions of one variable. Approximate continuity, approximate jump points, approximate differentiability.
25 Feb 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Structure of the distributional derivative, absolutely continuous, jump and Cantor part
04 Mar 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Approximate differentiability of BV functions, chain rule, trace operator.
11 Mar 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Characterization of BV and Sobolev functions by their behaviour on parallel lines. Pointwise properties of the precise representative
18 Mar 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Caccioppoli partitions, indecomposable components of sets of finite perimeter, Sobolev functions on nonsmooth domains, a short mention to the theory of SBV functions
25 Mar 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Theory of currents: preliminaries on multilinear algebra
01 Apr 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Top-dimensional currents, normal currents, real and integer rectifiable currents, flat currents.
08 Apr 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Characterization of flat currents with rectifiable support, properties of flat currents with finite mass (absolute continuity, locality, continuity)
29 Apr 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - A distanza
Slicing theorem and introduction to metric valued BV maps
06 Maggio 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Metric space valued maps, BV to Lipschitz property, Basic rectifiability criterion, Charcetrization of rectiafiable currents in terms of flatness and concentration of the mass measure
13 Maggio 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Commutation properties of slice and restriction and push forward. Proof of the closure theorem and of the boundary rectifiability theorem
27 Maggio 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Isoperimetric inequality, deformation theorem and existence of codimension-free and geometry-free isoperimetric constants
03 Giu 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Local minimizers, excess, introduction to the regularity theory
10 Giu 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Excess decay, tangent cones, Federer's dimension reduction argument
24 Giu 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Introduction to the theory of rectifiable varifolds. Monotonicity formula
09 Set 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Rectifiable varifolds, monotonicity formula and applications to Sobolev and Poincare' inequalities. Introduction to general varifolds
16 Set 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Rectifiability criteria for general varifolds, monotonicity and upper semicontinuity of the density
23 Set 2022 (2h 00m)
Luigi Ambrosio - Corso (attività didattica) - Mista
Compactness for integral varifolds, scketch of proof of Allard's theorem, via tilt lemma and excessy decay
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