Spring 2023
Dennis Kriventsov
Course Description:
The course 502 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).
Text:
#1. Haim Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. #2. Louis Nirenberg, Topics in Nonlinear Functional Analysis.
Prerequisites:
507 or permission by instructor
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Spring 2022
Hector Sussmann
Course Description:
This course will be a continuation of Math 16:640:507 Functional Analysis I. The course will develop the spectral theory of bounded and unbounded (not necessarily compact) self-adjoint operators, Sobolev spaces in N dimensions (with applications to elliptic boundary value problems), and spaces of distributions.
Text:
Functional Analysis, by H. Brezis
Prerequisites:
Math 507
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Spring 2020
Dennis Kriventsov
Course Description:
This course will be a continuation of Math 16:640:507 Functional Analysis I. The course will develop the spectral theory of bounded and unbounded (not necessarily compact) operators on Hilbert spaces, Sobolev spaces in N dimensions (with applications to elliptic boundary value problems), spaces of distributions, and other topics.
Text:
None
Prerequisites:
16:640:507 or equivalent
Schedule of Sections:
