Summer 2019 - MATH 895 G200
Class Number: 1996
Delivery Method: In Person
This course introduces the major techniques and theorems in nonlinear functional analysis, and how these arise/are used in the analysis of nonlinear partial differential equations and their discretizations. A particular focus of the course will be on variational techniques and nonlinear monotone operators.
COURSE-LEVEL EDUCATIONAL GOALS:
Fixed point theory: volume I
Nonlinear monotone operators: volume IIa from Nonlinear Functional Analysis, Zeidler
- strongly monotone operators (Chapter 1)
- quasilinear elliptic PDE (Chapter 2)
- Noncoercive equations, nonlinear Fredholm Alternatives (Chapter 5)
- Inner and outer approximation schemes (Chapter 7)
Variational methods: Volume III from Nonlinear Functional Analysis
- Chapters 1-8 and the generalized Kuhn-Tucker theory
There will be nine assignments; each assignment will be accompanied by a presentation in which students will present solutions. Eight of the nine assignments will each be worth 12.5% of the total grade (the ninth lowest will not count).
Zeidler, Eberhard. Nonlinear Functional Analysis Volumes i, iib, and iii.
Graduate Studies Notes:
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