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BV functions

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
Location: 
A-134
Next Lectures: 
Tuesday, December 6, 2022 - 09:00 to 11:00
Tuesday, December 13, 2022 - 09:00 to 11:00
Thursday, December 15, 2022 - 09:00 to 11:00
Tuesday, December 20, 2022 - 09:00 to 11:00
Thursday, December 22, 2022 - 09:00 to 11:00
Tuesday, January 10, 2023 - 09:00 to 11:00
Thursday, January 12, 2023 - 09:00 to 11:00
Tuesday, January 17, 2023 - 09:00 to 11:00
Thursday, January 19, 2023 - 09:00 to 11:00
Tuesday, January 24, 2023 - 09:00 to 11:00
Thursday, January 26, 2023 - 09:00 to 11:00
Tuesday, January 31, 2023 - 09:00 to 11:00
Thursday, February 2, 2023 - 09:00 to 11:00
Tuesday, February 7, 2023 - 09:00 to 11:00
Thursday, February 9, 2023 - 09:00 to 11:00
Tuesday, February 14, 2023 - 09:00 to 11:00
Thursday, February 16, 2023 - 09:00 to 11:00
Tuesday, February 21, 2023 - 09:00 to 11:00
Thursday, February 23, 2023 - 09:00 to 11:00

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