Learn · Advanced Partial Differential Equations - (Part I: Distributions and Sobolev Spaces)
Lecture 10 of 42Week 2 Fourier Transform and Topological Vector Spaces
Preliminaries-9
Prof. A. K. Nandakumaran and Prof. P. S. Datti · IISc Bangalore
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- Advanced Partial Differential Equations - (Part I: Distributions and Sobolev Spaces), IISc Bangalore (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Introduction-1
- Preliminaries-1
- Preliminaries-2
- Priliminaries-3
- Priliminaries-4
- Preliminaries-5
- Prelimunaries-6
- Preliminaries-7
- Preliminaries-8
- Preliminaries-9
- Introduction to Distributions
- Properties and Examples
- Convergence of distributions
- Convergence of distributions
- Calculus in the space of distributions
- Further discussion on Distributions
- Order and support of a distribution
- Laplace and Poisson equations - Distributions with compact support
- validity of the definition of the support
- Convolution and Fourier transform of distributions
- The Schwartz space and its dual
- Fourier transform of a tempered distribution, convolution
- Properties of Convolution
- Further discussion on Fourier transform and convolution
- Convolution of two distributions
- convolution of distributions
- Introduction to Sobolev spaces
- Properties of Sobloev Spaces
- Extension and Density results
- General Extension result
- Integration on a smooth surface
- A more general extension result
- Notion of the trace
- A compactness theorem
- Equivalent norms
- Sobolev lemma
- Sobolev lemma (continued)
- Analysis near the boundary
- Trace in the upper half space
- Trace in the upper half space
- Supplementary lecture
- Supplementary lecture