{"paper":{"title":"An optimization problem with volume constrain in Orlicz spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sandra Martinez","submitted_at":"2007-06-29T15:41:36Z","abstract_excerpt":"We consider the optimization problem of minimizing $\\int_{\\Omega}G(|\\nabla u|) dx$ in the class of functions $W^{1,G}(\\Omega)$, with a constrain on the volume of $\\{u>0\\}$. The conditions on the function $G$ allow for a different behavior at\n  0 and at $\\infty$. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution $u$ is locally Lipschitz continuous and that the free boundary, $\\partial\\{u>0\\}\\cap \\Omega$, is smooth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.4446","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"}