The course will cover more advanced topics in Functional Analysis and will include the following topics:
Part I: Functional Analysis for PDEs (Variational and Nonlinear Methods)
Distributions and Sobolev Spaces
• Linear Variational Problems
• Nonlinear Problems and Fixed-Point Theorems
Part II: Operator Theory and Evolution Problems
Bounded and Unbounded Operator Theory
• Semigroups of Operators (Hille-Yosida Theory)
• Applications to Evolution Equations
Part III: Harmonic Analysis
Interpolation Theory
• Littlewood-Paley Theory
• Calderón-Zygmund Theory
#1. Haim Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. #2. Sergiu Klainerman, Lecture Notes in Analysis
507 or 501 and permission of the instructor.