MAT 551: Real Analysis III - Partial Differential Equations
Department of Mathematics
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.
Stony Brook University
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),
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.
Class schedule: MW 2:30pm-3:50pm, ESS 079
Grades: Grades will be based on homeworks and class participation.
If you have a physical, psychological, medical or learning disability that may impact
your course work, please contact Disability Support Services, ECC (Educational Communications Center)
Building, room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary
and appropriate. All information and documentation is confidential. Students who require assistance during
emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services.
For procedures and information go to the following website:
Disability Support Services (DSS)
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