(MAT 1508S / APM 446S) An introduction to nonlinear partial differential equations as they arise in physics, geometry, and optimization. A key theme will be the development of techniques for studying non-smooth solutions to these equations, in which the nature of the non-smoothness or its absence is often the phenomenon of interest. The course will begin with a survey at the level of Evans' textbook, followed by an excursion into the mathematics of fluids.
References:
L.C. Evans "Partial Differential Equations" GSM 19 Providence AMS 1998, GSM 19
ISBN 0-8218-0772-2 $75 (\$60 AMS members)
A.J. Majda and A.L. Bertozzi "Vorticity and Incompressible Flow" Cambridge Univ. Press 2002. ISBN 0521639484 \$40