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An Introduction to the Theory of Functions of Bounded Variations

MA5948Elective Modules5 ECTSEnglishUnregelmäßigDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You learn the theory of functions of bounded variation (BV functions) and important tools from geometric measure theory. In the end you will be able to apply structural and compactness properties, traces and extensions as well as fine point properties of BV functions and sets with finite perimeter.

What you will be able to do

  • Understanding the structure of BV functions
  • Approximation by smooth functions
  • Application of the Coarea formula and isoperimetric inequality
  • Knowledge of reduced and measure-theoretic boundaries
  • Application of the Gauss-Green theorem for sets of finite perimeter
  • Analysis of pointwise properties: approximate continuity and differentiability

What the module consists of

  • VorlesungTransmission of theory and demonstrative examples
  • ÜbungWorking on examples and exercises for deepening under supervision

Teaching method

  • Blackboard-VorlesungPresentation of content in lectures with examples and discussion to stimulate own analysis
  • ÜbungssitzungenStudy of concrete examples and problem solving to firm up understanding
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Official page in TUMonline · Details are not binding.