Math 231AB-Partial Differential Equations, General Information
Fall, 2011 and Winter 2012
Course Description
These are the first two quarters of the year-long course on Partial Differential Equations. In the first half of Fall quarter the focus shall be on properties of the basic linear second order PDEs and introduction to quasi-linear first order PDEs. The second half shall be on Schauder's estimate, an introduction to Sobolev spaces and weak solutions to elliptic PDEs. Mainly we shall cover Chapters 2, 3, 5, part of 6 and 7 from Evans' book. Math 240, mainly the Lebesgue's integration ad differentiation theory is only required for the second half.
For Winter quarter we shall cover more advanced topics on elliptic and parabolic PDEs, which includes eigenvalues and eigenfunctions, L^p theory, Harnack inequalities for elliptic and parabolic equations, De Giorgi's theory, heat potential, boundary value problems for parabolic equation and systems.
There will be no exam. Your grade is based on homework assignments .
The complete course schedule will be available and updated weekly.
Instructors
| Name |
Office |
E-mail |
Phone |
Office Hours |
| Ni, Lei |
AP&M 5250 |
lni@math.ucsd.edu |
534-2704 |
MWF 2:00-2:50pm |
|
Course Time and Location
| Sections |
Instructor |
Time |
Place |
| Lecture |
Ni |
MWF 3:00pm-3:50 pm |
APM 5829 |
|
Texts
Required Text:
Partial Differential Equations, by Evans, AMS.
Second order equations of elliptic and parabolic type, by E. M. Landis, AMS, Translation of Mathematical Monographs.
Recommended other Texts:
Multiple Integrals in the Calculus of Variations, by Morrey, Springer.
Elliptic partial differential equations of second order, by Gilbarg and Trudinger, Springer
Some Related Papers :
R. Hamilton, J. Differential Geom. 1982.
P. Li and S.-T. Yau, Acta Math. 1987.
A. Grigor'yan, Math. USSR Sbornik. 1992.
G. Huisken and C. Sinestrari, Acta Math. 1999.
G. Perelman, The entropy formula for the Ricci flow and its geometric applications, Arxiv 0211159.
Homework
There will sets of homework assignment. You are asked to work them and return them back by the due dates. But you are encouraged to start to work on them once they are available.
Schedule
The course schedule will be updated weekly.
Grades
Grades will be based on the following percentages.
| Homework |
100% |
| Midterm Exam |
NO |
| Final Exam |
NO |
|
Last modified: Wed December 08, 14:49:08 PST 2009