Theory of Distribution and Sobolev Spaces

Code: MA745 | L-T-P-C: 4-0-0-8

MA745 Theory of Distribution and Sobolev Spaces [4-0-0-8] Prerequisites: Nil

Test Function and distribution: Definition, operations with distributions, convolution of distributions, Fourier transform of tempered distributions.

Sobolev spaces: Definition and properties, extension theorem, imbedding and completeness theorem, fractional order Sobolev spaces, trace theory. Application to Elliptic Problems: Weak solution of elliptic boundary value problem (BVP), regularity of weak solutions, maximum principle, eigenvalue problems, fixed point theorems and their application in semilinear elliptic BVP.

Texts:

1. R. A. Adams, Sobolev Spaces, Academic Press, 1975.
2. J. T. Oden and J.N. Reddy, An Introduction to Mathematical Theory of Finite Elements, Wiley Interscience, 1976.
3. S. Kesavan, Topics in Functional Analysis and Applications, Wiley Eastern Ltd. , New Delhi, 1989.
4. K. E. Brennan and R. Scott, The Mathematical Theory of Finite Element Methods, Springer-Verlag, Berlin, 1994.