Math 728 — Topics in PDEs

Elliptic Boundary Value Problems in Nonsmooth Domains

Fall 2002

Instructor: Irina Mitrea

Time: WF 1:25-2:40

Room: Malott 206

The scope of the course is to present an up-to-date, rigorous, and to a large extent self-contained, treatment of some of the most basic partial differential equations (PDE) of mathematical physics, via the modern tools of Harmonic Analysis. Examples include the Laplace equation, the Lamé system of elastostatics, the Stokes system of hydrostatics and the Maxwell system of electromagnetism.

We will review some of the tremendeous advances made in the last two decades in employing the classical method of layer potentials in the treatment of the boundary value problems associated with the aforementioned PDE in non-smooth domains in the euclidean setting.

The course is appropriate for anyone who has finished the analysis sequence Math 611 - 612.