{"paper":{"title":"Quasiconformal maps with controlled Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj, Eero Saksman","submitted_at":"2014-10-30T16:53:03Z","abstract_excerpt":"We establish that every $K$-quasiconformal mapping of $w$ of the unit disk $\\ID$ onto a $C^2$-Jordan domain $\\Omega$ is Lipschitz provided that $\\Delta w\\in L^p(\\ID)$ for some $p>2$. We also prove that if in this situation $K\\to 1$ with $\\|\\Delta w\\|_{L^p(\\ID)}\\to 0$, and $\\Omega \\to \\ID$ in $C^{1,\\alpha}$-sense with $\\alpha>1/2,$ then the bound for the Lipschitz constant tends to $1$. In addition, we provide a quasiconformal analogue of the Smirnov absolute continuity result over the boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8439","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"}