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Course Descriptions

16:640:518 - Partial Differential Equations II

Sagun Chanillo

Text:

There is no textbook for this course, suggested books are listed below.

Prerequisites:

501, 502, 503, 517, some very rudimentary Functional analysis

Description:

This will be a basic PDE course with a strong focus on basic estimates that lead to regularity and existence of solutions. I plan to cover Schauder theory of elliptic PDE, and attendant regularity theory. I hope to cover basic Sobolev spaces if it has not been covered in Math 517. I shall then also lecture on basic properties of pseudo-differential operators. The important theory of L^p regularity of solutions that is fundamental for the study of Nonlinear problems can only be covered if students have understood some Harmonic Analysis and the Calderon-Zygmund theory. If students have had some exposure to Harmonic Analysis, I will deal with the L^p theory, or else restrict myself to Schauder theory. No one book covers all this material. However, a good combination of books that has all this material is:

[1] Elliptic Partial Differential equations of Second Order, David Gilbarg and Neil S. Trudinger

[2] Introduction to Pseudodifferential and Fourier Integral Operators, Volume I, J. Francois Treves.

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530