{"paper":{"title":"Compactness of special functions of bounded higher variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Francesco Ghiraldin, Luigi Ambrosio","submitted_at":"2012-10-24T09:56:53Z","abstract_excerpt":"Given an open set \\Omega\\subset\\R^m and n>1, we introduce the new spaces GB_nV(\\Omega) of Generalized functions of bounded higher variation and GSB_nV(\\Omega) of Generalized special functions of bounded higher variation that generalize, respectively, the space B_nV introduced by Jerrard and Soner and the corresponding SB_nV space studied by De Lellis. In this class of spaces, which allow the description of singularities of codimension n, the distributional jacobian Ju need not have finite mass: roughly speaking, finiteness of mass is not required for the (m-n)-dimensional part of Ju, but only "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6473","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"}