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:

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.
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.