MAT 551: Real Analysis III - Partial Differential Equations

Fall 2018

Department of Mathematics
Stony Brook University

Topics Covered: Linear and nonlinear first order equations. Review of basic properties for the Laplace, heat, and wave operators. Existence and regularity theory for linear elliptic, hyperbolic, and parabolic equations. De Giorgi-Nash-Moser theory. General techniques for nonlinear equations: calculus of variations, fixed point theorems, continuity method, sub and super solutions, soft and hard implicit function theorems. Various applications to problems in geometry and physics.

References: 1) L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics Vol. 19, American Mathematical Society, Providence, RI, 1998.

2) D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, (2nd ed), Springer, 1983.

3) J. Kazdan, Applications of Partial Differential Equations to Problems in Geometry, Lecture Notes, University of Pennsylvania, 1993.

Instructor: Marcus Khuri, Math Tower 3-122. Office Hours: MW 4:00pm-5:00pm, F 2:00pm-3:00pm. Email: khuri@math.sunysb.edu

Class schedule: MW 2:30pm-3:50pm, ESS 079

Grades: Grades will be based on homeworks and class participation.

 
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