{"paper":{"title":"On the normal trace space of extended divergence-measure fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Christopher Irving","submitted_at":"2025-03-12T16:53:43Z","abstract_excerpt":"We characterise the normal trace space associated to extended (measure-valued) divergence-measure fields on the boundary of a set $E \\subset \\mathbb R^n$, as the Arens-Eells space $\\mathrm{AE}(\\partial E)$. Such a trace operator is constructed for any Borel set $E$, and under a mild regularity condition, which includes Lipschitz domains, this trace operator is shown to moreover be surjective. This relies in part on a new pointwise description of the Anzellotti pairing $\\overline{\\nabla \\phi \\cdot {\\boldsymbol F}}$ between a $\\mathrm{W}^{1,\\infty}$ function $\\phi$ and extended divergence-measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.09536","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.09536/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}