{"paper":{"title":"Neumann problems for nonlinear elliptic equations with $L^1$ data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anna Mercaldo, Maria Francesca Betta, Olivier Guib\\'e (LMRS)","submitted_at":"2014-10-02T19:38:22Z","abstract_excerpt":"In the present paper we prove existence results for solutions to nonlinear elliptic Neumann problems whose prototype is \\begin{equation*}\n  \\begin{cases}\n  -\\Delta_{p} u -\\text{div} (c(x)|u|^{p-2}u)) =f & \\text{in}\\ \\Omega, \\\\ \\left( |\\nabla u|^{p-2}\\nabla u+ c(x)|u|^{p-2}u \\right)\\cdot\\underline n=0 & \\text{on}\\ \\partial \\Omega \\,, \\end{cases} \\end{equation*} when $f$ is just a summable function. Our approach allows also to deduce a stability result for renormalized solutions and an existence result for operator with a zero order term."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0660","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"}