MA6090 Sobolev Spaces and applications to PDE


Course Details

Distribution Theory: Test functions and distributions, Convolution of Distributions, Tempered Distributions.
Sobolev Spaces: Definition and basic properties, Extension Theorems, Imbedding theorems, Compactness theorems, Trace theory.
Weak Solutions of Elliptic boundary value problems: Some abstract Variaitional problems, Examples of Elliptic BVPs, Existence and Regularity of weak solutions, Maximum principle, Eigenvalue problems.

Course References:

Text:
1. S. Kesavan, Topics in Functional Analysis and Applications, New Age International Publishers, 2015.
2. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011.
REFERENCES:
1. R.A Adams and J. F. Fournier, Sobolev Spaces, Academic Press, 2003.
2. W. Rudin, Functional Analysis, Tata McGraw-Hill, 2006.
3. R. S. Strichartz, A guide to Distribution Theory and Fourier Transforms, World Scientific, 2008.
4. M. Renardy and R. C. Rogers, An Introduction to Partial Differential Equations, Springer, 2004.