{"paper":{"title":"On planar Sobolev $L^m_p$-extension domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nahum Zobin, Pavel Shvartsman","submitted_at":"2014-10-12T15:22:36Z","abstract_excerpt":"For each $m\\ge 1$ and $p>2$ we characterize bounded simply connected Sobolev $L^m_p$-extension domains $\\Omega\\subset R^2$. Our criterion is expressed in terms of certain intrinsic subhyperbolic metrics in $\\Omega$. Its proof is based on a series of results related to the existence of special chains of squares joining given points $x$ and $y$ in $\\Omega$.\n  An important geometrical ingredient for obtaining these results is a new \"Square Separation Theorem\". It states that under certain natural assumptions on the relative positions of a point $x$ and a square $S\\subset\\Omega$ there exists a sim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3100","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"}