Theory and Applications of Sobolev Spaces

Code: MA664 | L-T-P-C: 3-0-0-6

Prerequisites: MA543 or equivalent

Theory of Sobolev spaces: Motivation, weak derivative, definition and basic properties of Sobolev spaces, extension theorem, embedding and compactness theorems, Dual spaces, fractional order Sobolev spaces, Trace theory. Methods for solving Elliptic boundary value problems: Weak solution of elliptic boundary value problem, regularity of weak solutions, maximum principle, eigenvalue problems. Solving elliptic boundary value problem using fixed point method, Galerkin method, monotone iteration method and variational method.

Texts/References:

1. R. A. Adams and J.J.F. Fournier, Sobolev Spaces, Academic Press, 2003.
2. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011.
3. S. Kesavan, Topics in Functional Analysis and Applications, New Age International Private Limited, 2015.