2006 Fall MATH 282-01
Bulletin Course Description Fourier transforms, distributions, elliptic equations, singular integrals, layer potentials, Sobolev spaces, regularity of elliptic boundary value problems. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title ELLIPTIC PDE Department MATH Course Number 2006 Fall 282 Section Number 01 Primary Instructor Stern,Mark A Permission required? N
Prerequisites
The student should have taken a real analysis course like our Math 241 and an introductory PDE course like PDE I (Math 232). Some acquaintance with functional
analysis is helpful, especially compact operators,
but will be reviewed at the beginning of the course.
Synopsis of course content
This course furnishes the tools needed in the study of elliptic P.D.E.'s such as Poisson's equation, but much of
what we study is used more generally.
We will begin with a review of the Fourier transform and distributions.
We review aspects of harmonic functions
and study the representation of solutions of
Laplacian u = f by singular integrals.
We will learn about Sobolev spaces
of functions having a certain number of derivatives
in a weak sense in L^2. We will then study existence
and regularity of elliptic boundary value problems
from this L^2 point of view. We will also show how to derive related results from a variational approach.
We will study asymptotic behavior of eigenfunctions of Schrodinger operators.
Further topics may be chosen from mildly nonlinear elliptic problems if time permits.
Textbooks
We will use the text by Folland, Introduction to
Partial Differential Equations, second edition.
Assignments
There will be regular written assignments.
Exams
There will probably not be an exam.
Grade to be based on
Written work.
