#### Abstract

The idea of Lusin approximation is applied to
the case of functions in the Sobolev spaces, which are shown to be
H\"older continuous except over small sets. The result matches in a
natural way with the Sobolev imbedding theorem and is well suited to
getextensions of some classical interior regularity results for
Poisson's equation.

*TUESDAY, November 13, 2001*

**Time:** 1:30 P.M.

**Location:** Physical Plant Building 300