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Journal Articles Indiana University Mathematics Journal Year : 2018

REMOVABLE SINGULARITIES FOR div v = f IN WEIGHTED LEBESGUE SPACES

Abstract

Let $w\in L^1_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p_{1/w}$, $1
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Dates and versions

hal-01214613 , version 1 (12-10-2015)

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Laurent Moonens, Emmanuel Russ, Heli Tuominen. REMOVABLE SINGULARITIES FOR div v = f IN WEIGHTED LEBESGUE SPACES. Indiana University Mathematics Journal, 2018, 67 (2), pp.859-887. ⟨10.1512/iumj.2018.67.6310⟩. ⟨hal-01214613⟩
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