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The Classical Isoperimetric Problem and its Nonlocal Variants

Course Type: 
PhD Course
Academic Year: 
2013-2014
Period: 
May-June
Duration: 
20 h
Description: 
  • Preliminary results on Geometric Measure Theory:
    • Hausdorff measures,
    • tangent measures, 
    • rectifiable sets.
  • The theory of sets of finite perimeter. 
  • The De Giorgi's solution to the Isoperimetric Problem. 
  • Partial regularity theory of Lambda-minimizers of the perimeter functional. 
  • A nonlocal variant of the perimeter: the sharp interface Ohta-Kawasaki energy. 
  • Regularity of  local minimizers. 
  • The second variation of the perimeter and of the Ohta-Kawasaki energy. 
  • Second order sufficiency conditions for local minimality. 
Location: 
A-133
Next Lectures: 

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