Calculus of Variations and Geometric Measure Theory
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S. Delladio

A note on enhanced density sets

created by delladio on 24 Jun 2009

[BibTeX]

Submitted Paper

Inserted: 24 jun 2009

Year: 2009

Abstract:

We give a simple proof of a statement extending this Fu's result: If $\Omega$ is a set of locally finite perimeter in $*R*^2$ then there is no function $f$ in $C^1(*R*^2)$ such that $Df (x_1,x_2)=(x_2,0)$ at a.e. $(x_1,x_2)$ in $\Omega$. We also prove that every measurable set can be approximated arbitrarily closely in $L^1$ by subsets which do not contain enhanced density points.

Keywords: Finite perimeter sets, enhanced density sets

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