Lusin approximation of Sobolev functions by Hölder continuous functions



Sergio Gutiérrez
Departmento de Matemática
Pontificia Universidad Católica de Chile
casilla 306
Santiago 22, Chile
email: sgutierr@mat.puc.cl



ABSTRACT:

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

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