{"paper":{"title":"Elliptic problems with growth in nonreflexive Orlicz spaces and with measure or $L^1$ data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Zatorska-Goldstein, Flavia Giannetti, Iwona Chlebicka","submitted_at":"2018-07-30T10:26:18Z","abstract_excerpt":"We investigate solutions to nonlinear elliptic Dirichlet problems of the type \\[ \\left\\{\\begin{array}{cl} - {\\rm div} A(x,u,\\nabla u)= \\mu &\\qquad \\mathrm{ in}\\qquad \\Omega, u=0 &\\qquad \\mathrm{ on}\\qquad \\partial\\Omega, \\end{array}\\right. \\] where $\\Omega$ is a bounded Lipschitz domain in $\\mathbb{R}^n$ and $A(x,z,\\xi)$ is a Carath\\'eodory's function. The growth of~the~monotone vector field $A$ with respect to the $(z,\\xi)$ variables is expressed through some $N$-functions $B$ and $P$. We do not require any particular type of growth condition of such functions, so we deal with problems in non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11275","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"}