Let $\Omega$ be an open subset of $R^n$, $n>1$, with finite measure and let $f:\Omega\to R^n$ be a Borel vector field on $\Omega$. Then, for every $\epsilon>0$, there exists a function $u$ on $\Omega$ of class $C^1$ such that $f$ agrees with the gradient $Du$ outside an open set of measure less than $\epsilon$.
A Lusin type theorem for gradients
ALBERTI, GIOVANNI
1991-01-01
Abstract
Let $\Omega$ be an open subset of $R^n$, $n>1$, with finite measure and let $f:\Omega\to R^n$ be a Borel vector field on $\Omega$. Then, for every $\epsilon>0$, there exists a function $u$ on $\Omega$ of class $C^1$ such that $f$ agrees with the gradient $Du$ outside an open set of measure less than $\epsilon$.File in questo prodotto:
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