{"paper":{"title":"Viscosity Solutions of Balanced Quasi-Monotone Fully Nonlinear Weakly Coupled Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andreas Minne, Martin H. Str\\\"omqvist","submitted_at":"2014-03-27T15:56:18Z","abstract_excerpt":"We introduce so called balanced quasi-monotone systems. These are systems $F(x,r,p,X)=(F_1(x,r,p,X),\\ldots,F_m(x,r,p,X))$, where $x$ belongs to a domain $\\Omega$, $r=u(x)\\in\\mathbb{R}^m$, $p=Du(x)$ and $X=D^2u(x)$, that can be arranged into two categories that are mutually competitive but internally cooperative. More precisely, for all $i\\neq j$ in the set $\\{1,2,\\ldots,m\\}$, $F_j$ is monotone non-decreasing (non-increasing) in $r_i$ if and only if $F_i$ is monotone non-decreasing (non-increasing) in $r_j$ and $F_j$ is a monotone function in $r_i$. We prove the existence and uniqueness of visc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7106","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"}