Sergio Gutierrez, Departamento de Matematicas, Pontificia Universidad Catolica de Chile.
"Lusin approximation of Sobolev functions by H\"older continuous functions"
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