{"paper":{"title":"Sobolev spaces on snowtrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.PR"],"primary_cat":"math.MG","authors_text":"Efstathios-Konstantinos Chrontsios-Garitsis, Vyron Vellis","submitted_at":"2026-06-29T21:21:59Z","abstract_excerpt":"We introduce a discrete-energy Sobolev space $\\mathcal{W}^{1,p}_{\\mathscr V}(T)$ on Ahlfors regular snowtrees, a class of metric trees where every arc is a snowflake of the same type. Our main result shows that, for every partition $\\mathscr V$ and every $1<p<\\infty$, this discrete space coincides quantitatively with the Korevaar--Schoen space on $T$. This fact and the independence of the space on the particular partition used to define $\\mathcal{W}^{1,p}_{\\mathscr V}(T)$ are both novel even for the class of geodesic trees. We also determine the critical Korevaar-Schoen exponent for Ahlfors re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30927","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/2606.30927/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"}