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BV functions and Sets of Finite Perimeter (WiSe 19/20)
Lectures (first one on October 15th): Tuesday, 14-16, Room H1.
Exercise classes (first one on October 17th): (every second) Thursday, 10-12, Room 415 (see on STINE for the exact dates).
Credits : 6 ECTS.
Prerequisites: Basic knowledge in measure theory and in the theory of Sobolev spaces is recommended, even though brief reminders shall be given when necessary.
(Tentative) Program:
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Fundaments of abstract Measure Theory (Hausdorff and Radon measures)
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Basic results from Geometric Measure Theory (Covering theorems, differentiation of measures, area and coarea formula)
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Functions of bounded variations (Approximation results, compactness and embeddings)
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Sets of finite perimeter (Reduced boundary, Blow-up, De Giorgi's Structure Theorem and rectifiability)
Literature:
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Luigi Ambrosio, Nicola Fusco, Diego Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, 2000.
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Lawrence C. Evans, Ronald F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 1992.
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Kenneth Falconer, Fractal geometry: mathematical foundations and applications, John Wiley & Sons, 2004.
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Enrico Giusti, Functions of Bounded Variation and Minimal Surfaces, Birkhäuser, 1984.
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Francesco Maggi, Sets of Finite Perimeter and Geometric Variational Problems, Cambridge University Press, 2012.
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Elias M. Stein, Rami Shakarchi, Real analysis: measure theory, integration, and Hilbert spaces, Princeton University Press, 2009.
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William P. Ziemer, Weakly Differentiable Functions, Springer, 1989.
The exercise sheet will be uploaded on STINE every second Wednesday. The submission day is every second Tuesday at the beginning of the lecture.
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