{"paper":{"title":"A minimum problem with free boundary and subcritical growth in Orlicz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Jun Zheng, Leandro S. Tavares","submitted_at":"2018-09-23T02:50:18Z","abstract_excerpt":"The aim of this paper is to study the heterogeneous optimization problem\n  \\begin{align*} \\mathcal {J}(u)=\\int_{\\Omega}(G(|\\nabla u|)+qF(u^+)+hu+\\lambda_{+}\\chi_{\\{u>0\\}} )\\text{d}x\\rightarrow\\text{min}, \\end{align*} in the class of functions $ W^{1,G}(\\Omega)$ with $ u-\\varphi\\in W^{1,G}_{0}(\\Omega)$, for a given function $\\varphi$, where $W^{1,G}(\\Omega)$ is the class of weakly differentiable functions with $\\int_{\\Omega}G(|\\nabla u|)\\text{d}x<\\infty$. The functions $G$ and $F$ satisfy structural conditions of Lieberman's type that allow for a different behavior at $0$ and at $\\infty$. {}{Mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08518","kind":"arxiv","version":2},"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"}