{"paper":{"title":"The structure of ${\\cal A}$-free measures with uniformly singular part","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Darko Mitrovic","submitted_at":"2016-12-31T09:21:50Z","abstract_excerpt":"We prove that a singular part $\\mu_s$ of a measure $\\mu$ satisfying ${\\cal A}\\mu =0$ for a linear partial differential operator ${\\cal A}$ defined on $R^d$ has the range in the intersection of kernels of the principal symbol of ${\\cal A}$ if the singular part is singular with respect to all the variables (uniformly singular) i.e. it is such that for $\\mu_s$-almost every $x\\in R^d$ there exist positive functions $\\alpha(\\epsilon), \\beta(\\epsilon)$, $\\epsilon \\in R$, satisfying $\\frac{\\alpha(\\epsilon)}{\\epsilon}\\to 0$, $ \\frac{\\epsilon}{\\beta(\\epsilon)}\\to 0$ and a set $E_\\epsilon\\subset B(\\mx,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00078","kind":"arxiv","version":2},"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"}