{"paper":{"title":"Symmetry of Convex Solutions to Fully Nonlinear Elliptic Systems: Unbounded Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Weijun Zhang, Zhitao Zhang","submitted_at":"2024-04-01T15:39:58Z","abstract_excerpt":"In this paper, we are concerned with the monotonic and symmetric properties of convex solutions Monge-Amp\\`ere systems for instance, considering\n  \\begin{equation*}\n  \\det(D^2u^i)=f^i(x,{\\bf u},\\nabla u^i), \\ 1\\leq i\\leq m,\n  \\end{equation*} over unbounded domains of various cases, including the whole spaces $\\mathbb{R}^n$, the half spaces $\\mathbb{R}^n_+$ and the unbounded tube shape domains in $\\mathbb{R}^n$. We obtain monotonic and symmetric properties of the solutions to the problem with respect to the geometry of domains and the monotonic and symmetric properties of right-hand side terms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.01185","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.01185/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}