{"paper":{"title":"Uniqueness of absolute minimizers for $L^\\fz$-functionals involving Hamiltonians $H(x,p)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changyou Wang, Qianyun Miao, Yuan Zhou","submitted_at":"2015-09-15T01:37:50Z","abstract_excerpt":"For a bounded domain $U\\subset\\rn$, consider the\n  $L^\\fz$-functional involving a nonnegative Hamilton function $H:\\overline U\\times\\rn\\to [0,\\fz)$. In this paper, we will establish the uniqueness of absolute minimizers $u\\in W^{1,\\fz}_\\loc(U)\\cap C(\\overline U)$ for $H$, under the Dirichlet boundary value $g\\in C(\\partial U)$, provided\n  \\noindent (A1) $H$ is lower semicontinuous in $\\overline U\\times\\rn$, and $H(x,\\cdot)$ is convex for any $x\\in\\overline U$.\n  \\noindent (A2) $\\displaystyle H(x,0)=\\min_{p\\in \\rn}H(x,p)=0$ for any $ x\\in \\overline U$, and $\\displaystyle\\bigcup_{x\\in \\overline "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04371","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"}