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.
Disability Support Services (DSS)
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:
http://www.stonybrook.edu/ehs/fire/disabilities
Academic Integrity
Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances
of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management,
Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more
comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary
website at
http://www.stonybrook.edu/commcms/academic_integrity/index.html
Critical Incident Management
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to
report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of
the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required
to follow their school-specific procedures.