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arXiv · 1510.03544

Removable singularities for div v = f in weighted Lebesgue spaces

Laurent Moonens·Emmanuel Russ·Heli Tuominen
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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 $L^p\_{1/w}$, $1\textless{}p\textless{}+\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author.

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Laurent Moonens, Emmanuel Russ, Heli Tuominen. 2015-10-13. Removable singularities for div v = f in weighted Lebesgue spaces. https://arxiv.org/abs/1510.03544

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