Lecturer:
Course Type:
PhD Course
Academic Year:
2022-2023
Period:
October - March
Duration:
60 h
Description:
- Vector valued Radon measures
- Notions of weak convegrence of measures
- 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 with finite perimeter by smooth sets
- Embedding theorems and isoperimetric inequalities
- Coarea formula
- Traces of BV functions
- Carathéodory costruction
- Hausdorff measures and comparison with Lebesgue mesasure
- Convex functions of measures and their semicontinuity
- Relaxation in BV of functionals depending on the gradient
- Lebesgue points of a BV function
- Rectifiability of the jump set of a BV function
- Behaviour of a BV function near a jump point
- Decomposition of the gradient of a BV function
- The space SBV
- Slicing of BV functions
- Compactness theorem for SBV
- Lower semicountinuity of the measure of the jump set
- The Mumford-Shah problem
Research Group:
Location:
A-134