{"paper":{"title":"A Bounded Linear Extension Operator for $L^{2,p}(\\R^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Arie Israel","submitted_at":"2010-11-02T18:02:52Z","abstract_excerpt":"For a finite $E \\subset \\R^2$, $f:E \\rightarrow \\R$, and $p>2$, we produce a continuous $F:\\R^2 \\rightarrow \\R$ depending linearly on $f$, taking the same values as $f$ on $E$, and with $L^{2,p}(\\R^2)$ semi-norm minimal up to a factor $C=C(p)$. This solves the Whitney extension problem for the Sobolev space $L^{2,p}(\\R^2)$. A standard method for solving extension problems is to find a collection of local extensions, each defined on a small square, which if chosen to be mutually consistent can be patched together to form a global extension defined on the entire plane. For Sobolev spaces the sta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0689","kind":"arxiv","version":2},"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"}