{"paper":{"title":"On a decomposition of regular domains into John domains with uniform constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Manuel Friedrich","submitted_at":"2016-04-30T16:01:35Z","abstract_excerpt":"We derive a decomposition result for regular, two-dimensional domains into John domains with uniform constants. We prove that for every simply connected domain $\\Omega \\subset {\\Bbb R}^2$ with $C^1$-boundary there is a corresponding partition $\\Omega = \\Omega_1 \\cup \\ldots \\cup \\Omega_N$ with $\\sum_{j=1}^N \\mathcal{H}^1(\\partial \\Omega_j \\setminus \\partial \\Omega) \\le \\theta$ such that each component is a John domain with a John constant only depending on $\\theta$. The result implies that many inequalities in Sobolev spaces such as Poincar\\'e's or Korn's inequality hold on the partition of $\\O"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00130","kind":"arxiv","version":3},"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"}