Math 657: Nonlinear Partial Differential Equations (Winter 2008)

Make-up classes: Monday April 7 and April 14, 2:30 pm to 4 pm in 216 Dennison Homework

Instructor

Name: Volker Elling
Office: East Hall 4063
Office hours: TTh 2-3:30 pm or by appointment, walk-ins welcome
Office phone: (734)764-0366
Uniqname: velling (for contact by email etc)

Class

Time: TTh 11:30 am -- 1 pm
Room: East Hall 4096

Content

This course is designed to give students a ``general education'' in nonlinear PDE and to prepare some of them for research in this area. Nonlinear PDE is a wide area; much of the theory focuses on particular problems with relatively little connection to others. In this course preference is given to foundations and to widely applicable techniques. Topics (subject to change based on progress): Sobolev spaces, energy methods for nonlinear PDE, Euler-Lagrange equations, linear elliptic PDE, Hölder spaces and Schauder estimates, Fredholm theory, maximum principles, nonlinear elliptic PDE, method of continuity, Leray-Schauder degree, variational problems, monotonicity. Subject to changes depending on available time.

Prerequisites: good preparation in real analysis, measure theory, some functional analysis (Banach spaces). Math 656 is useful, but not necessary.

Books

There is no single textbook for the course. The following references may be helpful.

Evans, Partial Differential Equations
Folland, Introduction to Partial Differential Equations
Gilbarg/Trudinger, Elliptic Partial Differential Equations of Second Order
McOwen, Partial Differential Equations
Taylor, Partial Differential Equations III: Nonlinear Equations
Smoller, Reaction-Diffusion Equations and Shock Waves

Functional analysis:

Heuser, Functional analysis
Kato, Perturbation Theory for Linear Operators
Yosida, Functional Analysis

Real analysis/measure theory:

Hewitt/Stromberg, Real and Abstract Analysis

Grading and policies

Grading is based on attendance and a few homework sets.