Math 2.0

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Advanced Partial Differential Equations – (Part I: Distributions and Sobolev Spaces) J1D851YBRM

URIm2://res/J1D851YBRM
Kindcourse
CreatorsP.S. Datti (instructor), A. K. Nandakumaran (instructor)
Date2023-07-03
MSC35-XX
Scopein
Idscourse 04dese585:111108168

Expressions

e1: edition

Languageen
Date2023-07-03
Contents
  • part 1: Week 1 Bascis Real and Functional Analysis
  • session 1: Introduction-1
  • session 2: Preliminaries-1
  • session 3: Preliminaries-2
  • session 4: Priliminaries-3
  • session 5: Priliminaries-4
  • part 2: Week 2 Fourier Transform and Topological Vector Spaces
  • session 6: Preliminaries-5
  • session 7: Prelimunaries-6
  • session 8: Preliminaries-7
  • session 9: Preliminaries-8
  • session 10: Preliminaries-9
  • part 3: Week 3 Distributions
  • session 11: Introduction to Distributions
  • session 12: Properties and Examples
  • session 13: Convergence of distributions
  • session 14: Convergence of distributions
  • session 15: Calculus in the space of distributions
  • part 4: Week 4 Order and support of distributions
  • session 16: Further discussion on Distributions
  • session 17: Order and support of a distribution
  • session 18: Laplace and Poisson equations - Distributions with compact support
  • session 19: validity of the definition of the support
  • session 20: Convolution and Fourier transform of distributions
  • part 5: Week 5 Convolution and Fourier transform of Distributions
  • session 21: The Schwartz space and its dual
  • session 22: Fourier transform of a tempered distribution, convolution
  • session 23: Properties of Convolution
  • session 24: Further discussion on Fourier transform and convolution
  • session 25: Convolution of two distributions
  • part 6: Week 6 Sobolev Spaces
  • session 26: convolution of distributions
  • session 27: Introduction to Sobolev spaces
  • session 28: Properties of Sobloev Spaces
  • session 29: Extension and Density results
  • session 30: General Extension result
  • part 7: Week 7 Extension result and compact embeddings
  • session 31: Integration on a smooth surface
  • session 32: A more general extension result
  • session 33: Notion of the trace
  • session 34: A compactness theorem
  • session 35: Equivalent norms
  • session 36: Sobolev lemma
  • part 8: Week 8 Trace theory
  • session 37: Sobolev lemma (continued)
  • session 38: Analysis near the boundary
  • session 39: Trace in the upper half space
  • session 40: Trace in the upper half space
  • session 41: Supplementary lecture
  • session 42: Supplementary lecture

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