{"paper":{"title":"Korevaar-Schoen and heat kernel characterizations of Sobolev and BV spaces on local trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MG","math.PR"],"primary_cat":"math.AP","authors_text":"Fabrice Baudoin, Li Chen, Meng Yang","submitted_at":"2025-05-15T11:08:58Z","abstract_excerpt":"We study Sobolev and BV spaces on local trees which are metric spaces locally isometric to real trees. Such spaces are equipped with a Radon measure satisfying a locally uniform volume growth condition. Using the intrinsic geodesic structure, we define weak gradients and develop from it a coherent theory of Sobolev and BV spaces. We provide two main characterizations: one via Korevaar-Schoen-type energy functionals and another via the heat kernel associated with the natural Dirichlet form. Applications include interpolation results for Besov-Lipschitz spaces, critical exponents computations, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10177","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.10177/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"}