{"paper":{"title":"Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J. V. Goncalves, M. L. M. Carvalho","submitted_at":"2013-10-22T13:07:52Z","abstract_excerpt":"We develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation $\\displaystyle -\\mbox{div} (\\phi(|\\nabla u|) \\nabla u) = f(x,u) + h \\mbox{in} \\Omega$ under Dirichlet boundary conditions, where $\\Omega \\subset {\\bf R}^{N}$ is a bounded smooth domain, $\\phi : (0,\\infty)\\longrightarrow (0,\\infty)$ is a suitable continuous function and $f: \\Omega \\times {\\bf R} \\to {\\bf R}$ satisfies the Carath\\'eodory conditions, while $h$ is a measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5907","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"}