MTH-204.4 Advanced Functional Analysis

Distribution theory, Sobolev Spaces, embedding theorems, Rellich's lemma, trace theorems.

Second order elliptic equations:- Formulation of Dirichlet, Neumann and oblique derivative problems, Weak formulation, Lax - Milgram Lemma, existence and regularity up to the boundary, maximum principle, elementary variational inequality.

Linear evolution equations, existence of weak solutions, energy methods.