{"paper":{"title":"On Boman's Theorem On Partial Regularity Of Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CV","authors_text":"Tejinder Neelon","submitted_at":"2011-04-14T17:48:24Z","abstract_excerpt":"Let {\\Lambda}\\subsetR^{n}\\timesR^{m} and k be a positive integer. Let f:R^{n}\\rightarrowR^{m} be a locally bounded map such that for each ({\\xi},{\\eta})\\in{\\Lambda}, the derivatives D_{{\\xi}}^{j}f(x):=|((d^{j})/(dt^{j}))f(x+t{\\xi})|_{t=0}, j=1,2,...k, exist and are continuous. In order to conclude that any such map f is necessarily of class C^{k} it is necessary and sufficient that {\\Lambda} be not contained in the zero-set of a nonzero homogenous polynomial {\\Phi}({\\xi},{\\eta}) which is linear in {\\eta}=({\\eta}_{1},{\\eta}_{2},...,{\\eta}_{m}) and homogeneous of degree k in {\\xi}=({\\xi}_{1},{\\x"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2847","kind":"arxiv","version":3},"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"}