{"paper":{"title":"$C^\\infty$ local solutions of elliptical $2-$Hessian equation in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao-Jiang Xu (LMRS), Guiji Tian, Qi Wang","submitted_at":"2014-06-13T19:30:12Z","abstract_excerpt":"In this work, we study the existence of $C^{\\infty}$ local solutions to $2$-Hessian equation in $\\mathbb{R}^{3}$. We consider the case that the right hand side function $f$ possibly vanishes, changes the sign, is positively or negatively defined. We also give the convexities of solutions which are related with the annulation or the sign of right-hand side function $f$. The associated linearized operator are uniformly elliptic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3613","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"}