After successful completion of the course, students are able to approach several research topics in the calculus of variations, such as image reconstruction, modeling of fracture mechanics, and equilibrium shapes of liquids and sessile drops.
-Vector valued Radon measures and weak convergence-Definition of BV and of perimeter-Semicontinuity of the perimeter and of the total variation-Approximation of BV functions by smooth functions-Approximation of sets of finite perimeter by smooth sets-Isoperimetric inequality and Coarea formula-Traces of BV functions-Reduced boundary and De Giorgi's structure theorem-Lebesgue points of a BV function-Behaviour of a BV function near the jump set-Decomposition of the gradient of a BV function
The course consists of 12 frontal meetings of two hours per week. Lessons will mainly focus on the techniques and ideas underlying the BV-theory. Material will be provided for further study.
During the first lecture we will decide the schedule of the course.
Students can agree with the lecturer on a in-depth research topic which will be presented as a seminar.
Not necessary
Some knowledge on basic geometric measure theory could be helpful. For instance, Lebesgue's points of an integrable function, notion of Hausdorff measure, and differentiation of measures.
