{"paper":{"title":"Symmetry results for stable and monotone solutions to fibered systems of PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Pinamonti, Serena Dipierro","submitted_at":"2012-12-03T15:01:50Z","abstract_excerpt":"We study the symmetry properties for solutions of elliptic systems of the type\n{ll}-\\dive(a_1(x,|\\nabla u^1|(X))\\nabla u^1(X))=F_{1}(x, u^1(X),..., u^n(X)),\n...\n-\\dive(a_n(x,|\\nabla u^n|(X))\\nabla u^n(X))=F_{n}(x, u^1(X),..., u^n(X)),\nwhere $x\\in \\R^m$ with $1\\leq m< N$, $X=(x,y)\\in \\R^m\\times \\R^{N-m}$, and $F_{1},..., F_{n}$ are the derivatives with respect to $\\xi^1,..., \\xi^n$ of some $F=F(x,\\xi^1,..., \\xi^n)$ such that for any $i=1,..., n$ and any fixed $(x,\\xi^1,..., \\xi^{i-1},\\xi^{i+1},..., \\xi^n)\\in \\R^m\\times \\R^{n-1}$ the map $\\xi^i\\to F(x,\\xi^1,...,\\xi^i,..., \\xi^n)$ belongs to $C^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0408","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"}