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Sets of finite perimeter, Gauss-Green theorem, pointwise properties of BV functions, Stokes theorem for
nonsmooth data, rectifiability, definition of currents. Recommended for master students of mathematical analysis.
Last update: T_KMA (02.05.2013)
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The exam is oral. The required knowledge corresponds to the sylabus at the extent of lectures and home reading. In case of distant exam this will consist in solving a theoretical problem in real time. Sample problems will be sent within May.
Last update: Malý Jan, prof. RNDr., DrSc. (30.04.2020)
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L. Ambrosio, N. Fusco, D. Pallara: Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 2000.
H. Federer: Geometric measure theory. Classics in Mathematics, Springer 1996.
L.C. Evans, R.F. Gariepy: Measure theory and fine properties of functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1992 Last update: Kaplický Petr, doc. Mgr., Ph.D. (09.06.2015)
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The exam is oral. The required knowledge corresponds to the sylabus at the extent of lectures and home reading. In case of distant exam this will consist in solving a theoretical problem in real time. Sample problems will be sent within May.
Last update: Malý Jan, prof. RNDr., DrSc. (30.04.2020)
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1. Rectifiable sets
Rectifiability
Tangent spaces
C-1 approximation
Densities
Differential forms and currents
2. BV functions of several variables
Essential variations on lines
Convergence of BV functions (strong, weak, strict)
Pointwise properties of BV functions
3. Sets of finite perimeter
Federer boundary and its rectifiability
Gauss-Green theorem
Characterization by the essential boundary
4. Lipschitz manifolds
Lipschitz atlas
Orientation
Stokes theorem Last update: Kaplický Petr, doc. Mgr., Ph.D. (09.06.2015)
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Measures, Radon-Nikodym theorem, Lebesgue integral, Radon measures, convolution, smoothing by convolution, strong, weak and weak* convergence in Banach spaces, theory of distributions, Lipschitz functions and mappings, Hausdorff measure, L^p spaces and spaces of continuous functions, area and coarea formula Last update: Malý Jan, prof. RNDr., DrSc. (10.05.2018)
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