REMOVABLE SINGULARITIES FOR div v = f IN WEIGHTED LEBESGUE SPACES
Résumé
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
Soumis le : lundi 12 octobre 2015-16:07:02
Dernière modification le : mercredi 18 décembre 2024-09:28:42
Archivage à long terme le : mercredi 13 janvier 2016-12:40:34
Dates et versions
Identifiants
- HAL Id : hal-01214613 , version 1
- ARXIV : 1510.03544
- DOI : 10.1512/iumj.2018.67.6310
Citer
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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