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Differentiablity of Lipschitz Functions on Metric Measure Spaces

Niakan Pak, Mahdi | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41773 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Ranjbar Motlagh, Alireza
  7. Abstract:
  8. In this thesis, vve generali :ed the notion of (upper) gradient to arbitrary func- tions on a. metric measure space a.nd under some conditions -vve study deriva- t.ives of Lipschitz functions and their differential properties. Finally, we consider metric measure spaces that satisfy certa.in additiona.l conditions and give more detailed study of these notions
  9. Keywords:
  10. Poincare Inequality ; Lipschitz Map ; Metric Space ; Upper Gradient ; Doubling Condition

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