The course 508 is a continuation of Fall’s 507.
We will pick up where the course 507 ended. Will do the following:
#1. Followthe the book of Haim Brezis "Functional Analysis, Sobolev Spaces and Partial Differential Equations" starting from where 507 ended (Hill-Yosida Theorem, Sobolev Spaces and the Variational Formulation of Boundary Value Problem, The Heat and the Wave Equation)
#2. Presenting Chapter 1-3 of Louis Nirenberg's Lecture Notes on "Topics in Nonlinear Functional Analysis" (Sard's Theorem, Brouwer Degree, Leray-Schauder Degree and Applications to PDEs, Lyapunov-Schmidt Procedure and nonlinear version+ gluing of approximate solutions into genuine solutions, Morse Lemma, a local bifurcation theorem of Krasnoselski, a global bifurcation theorem of Rabinowitz).
#1. Haim Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. #2. Louis Nirenberg, Topics in Nonlinear Functional Analysis.
507 or permission by instructor