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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https://hal.science/hal-01214613
Submitted on : Monday, October 12, 2015-4:07:02 PM
Last modification on : Friday, March 24, 2023-2:53:01 PM
Long-term archiving on: Wednesday, January 13, 2016-12:40:34 PM
Cite
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. ⟨hal-01214613⟩
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