{"paper":{"title":"A look into some of the fine properties of functions with bounded $\\mathscr A$-variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adolfo Arroyo-Rabasa, Anna Skorobogatova","submitted_at":"2019-11-19T18:56:37Z","abstract_excerpt":"We establish certain fine properties for functions of bounded $\\mathscr A$-variation known in the classical $BV$ setting. Here, $\\mathscr A$ is a $k$th order constant-coefficient homogeneous linear differential operator with a finite-dimensional kernel (also known as a complex-elliptic operator). We prove that if $\\mathscr Au$ can be represented by a finite Radon measure, then the potential $u$ has one-sided $L^p$-approximate limits on Lipschitz hypersurfaces, and, more generally, on countably rectifiable sets of codimension one. We use this to give pointwise characterizations of the (function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.08474","kind":"arxiv","version":4},"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/1911.08474/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"}