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BV functions

Lecturer: 
Course Type: 
PhD Course
Academic Year: 
2018-2019
Period: 
October-February
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
Location: 
A-133

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