Sobolev Spaces
October - December 2011. Professor G Burton.
Topics:
- Distributions and their partial derivatives.
- Distributional derivatives of functions.
- Weak solutions of partial differential equations.
- Sobolev spaces.
- Convolution.
- Mollification.
- Density of smooth functions in Sobolev spaces.
- Sobolev inequality.
- Embeddings.
- Poincare inequality.
- Rellich-Kondrachov compact embedding theorem.
- Simple examples on existence of weak solutions.
- Boundary values of Sobolev functions.
- Use of weak compactness
Course Assessment:
The course will be assessed by viva.
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