{"paper":{"title":"Convex integration with linear constraints and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Seonghak Kim","submitted_at":"2016-05-08T17:28:53Z","abstract_excerpt":"We study solutions of the first order partial differential inclusions of the form $\\nabla u\\in K$, where $u:\\Omega\\subset\\mathbb{R}^n\\to\\mathbb{R}^m$ and $K$ is a set of $m\\times n$ real matrices, and derive a companion version to the result of {M\\\"uller and \\v{S}ver\\'ak} [20], concerning a general linear constraint on the components of $\\nabla u$. We then consider two applications: the vectorial eikonal equation and a $T_4$-configuration both under linear constraints."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02340","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"}