This course will rapidly review the basics of Sobolev spaces. Then we will study Calderon-Zygmund estimates. Following this we will apply the previous two topics to study elliptic boundary value problems on smooth, bounded domains. The last topic will be to study Strichartz inequalities and some applications to wave and Schrodinger equations.
Suggested: Elliptic Second Order PDE, by David Gilbarg and N. S. Trudinger
A sound knowledge of basic real variables, 501, 502. It will be very helpful if the student is familiar with 507 functional analysis and 517 the PDE course.