{"paper":{"title":"Removable singularities for div v = f in weighted Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Emmanuel Russ (IF), Heli Tuominen, Laurent Moonens (LM-Orsay)","submitted_at":"2015-10-13T06:10:57Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03544","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}