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.