{"paper":{"title":"Sobolev regularity of quasiconformal mappings on domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Mart\\'i Prats","submitted_at":"2015-07-15T19:14:18Z","abstract_excerpt":"Consider a Lipschitz domain $\\Omega$ and a measurable function $\\mu$ supported in $\\overline\\Omega$ with $\\left\\|{\\mu}\\right\\|_{L^\\infty}<1$. Then the derivatives of a quasiconformal solution of the Beltrami equation $\\overline{\\partial} f =\\mu \\partial f$ inherit the Sobolev regularity $W^{n,p}(\\Omega)$ of the Beltrami coefficient $\\mu$ as long as $\\Omega$ is regular enough. The condition obtained is that the outward unit normal vector $N$ of the boundary of the domain is in the trace space, that is, $N\\in B^{n-1/p}_{p,p}(\\partial\\Omega)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04332","kind":"arxiv","version":4},"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"}