{"paper":{"title":"On the interpolation space $(L^p(\\Omega), W^{1,p}(\\Omega))_{s,p}$ in non-smooth domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Irene Drelichman, Ricardo G. Dur\\'an","submitted_at":"2017-10-25T20:40:16Z","abstract_excerpt":"We show that, for certain non-smooth bounded domains $\\Omega\\subset\\mathbb{R}^n$, the real interpolation space $(L^p(\\Omega), W^{1,p}(\\Omega))_{s,p}$ is the subspace $\\widetilde W^{s,p}(\\Omega) \\subset L^p(\\Omega)$ induced by the restricted fractional seminorm $$ |f|_{\\widetilde W^{s,p}(\\Omega)} = \\Big( \\int_\\Omega \\int_{|x-y|<\\frac{d(x)}2} \\frac{|f(x)-f(y)|^p}{|x-y|^{n+sp}} \\, dy \\,dx \\Big)^\\frac{1}{p}. $$ In particular, the above result includes simply connected uniform domains in the plane, for which a characterization of the interpolation space was previously unknown."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09453","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"}