{"paper":{"title":"Sobolev homeomorphisms with gradients of low rank via laminates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Mora-Corral, Daniel Faraco, Marcos Oliva","submitted_at":"2016-03-13T16:30:31Z","abstract_excerpt":"Let $\\Omega\\subset \\mathbb{R}^{n}$ be a bounded open set. Given $2\\leq m\\leq n$, we construct a convex function $\\phi :\\Omega\\to \\mathbb{R}$ whose gradient $f= \\nabla \\phi$ is a H\\\"older continuous homeomorphism, $f$ is the identity on $\\partial \\Omega$, the derivative $D f$ has rank $m-1$ a.e.\\ in $\\Omega$ and $D f$ is in the weak $L^{m}$ space $L^{m,w}$. The proof is based on convex integration and staircase laminates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04047","kind":"arxiv","version":1},"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"}