{"paper":{"title":"A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Giovanni E. Comi, G. Stefani","submitted_at":"2019-10-29T17:33:58Z","abstract_excerpt":"We continue the study of the space $BV^\\alpha(\\mathbb{R}^n)$ of functions with bounded fractional variation in $\\mathbb{R}^n$ of order $\\alpha\\in(0,1)$ introduced in arXiv:1809.08575, by dealing with the asymptotic behaviour of the fractional operators involved. After some technical improvements of certain results of our previous work, we prove that the fractional $\\alpha$-variation converges to the standard De Giorgi's variation both pointwise and in the $\\Gamma$-limit sense as $\\alpha\\to1^-$. We also prove that the fractional $\\beta$-variation converges to the fractional $\\alpha$-variation b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.13419","kind":"arxiv","version":5},"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/1910.13419/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"}