{"paper":{"title":"A generalization of an integrability theorem of Darboux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Helge Kristian Jenssen, Irina A. Kogan, Michael Benfield","submitted_at":"2018-03-24T18:44:12Z","abstract_excerpt":"In his monograph \"Le\\c{c}ons sur les syst\\`emes orthogonaux et les coordonn\\'ees curvilignes. Principes de g\\'eom\\'etrie analytique\", 1910, Darboux stated three theorems providing local existence and uniqueness of solutions to first order systems of the type \\[\\partial_{x_i} u_\\alpha(x)=f^\\alpha_i(x,u(x)),\\quad i\\in I_\\alpha\\subseteq\\{1,\\dots,n\\}.\\] For a given point $\\bar x\\in \\mathbb{R}^n$ it is assumed that the values of the unknown $u_\\alpha$ are given locally near $\\bar x$ along $\\{x\\,|\\, x_i=\\bar x_i \\, \\text{for each}\\, i\\in I_\\alpha\\}$. The more general of the theorems, Th\\'eor\\`eme II"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09147","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"}