Functions of Bounded Variations and Applications

What it is about

You will learn the fundamentals and important tools of the theory of functions of bounded variation as well as geometric measure theory. You will understand measures such as Hausdorff measures, area and Coarea formulas, concepts of sets of finite perimeter and special BV functions. In the end you will be able to apply these terms to the treatment of relaxation problems in W^{1,1} and understand the mathematics behind the Mumford–Shah functional.

What you will be able to do

• Understand concepts of functions of bounded variation (BV)
• Analyze sets of finite perimeter
• Apply Hausdorff measures and basic concepts of geometric measure theory
• Apply area- and Coarea-formulas
• Understand relaxations for functionals in W^{1,1}
• Explain mathematical foundations of the Mumford–Shah functional

What the module consists of

• VorlesungPresentation of content, demonstrative examples and discussions; weekly exercises
• Skript/ÜbungenAdditional material and tasks are provided and available on Moodle

Teaching method

• Blackboard lecturesLecture with examples and discussions, encouraging independent analysis and self-study