{"paper":{"title":"Remarks on some quasilinear equations with gradient terms and measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Laurent Veron (LMPT), Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Marta Garcia-Huidobro","submitted_at":"2012-11-28T08:31:24Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^{N}$ be a smooth bounded domain, $H$ a Caratheodory function defined in $\\Omega \\times \\mathbb{R\\times R}^{N},$ and $\\mu $ a bounded Radon measure in $\\Omega .$ We study the problem% \\begin{equation*} -\\Delta_{p}u+H(x,u,\\nabla u)=\\mu \\quad \\text{in}\\Omega,\\qquad u=0\\quad \\text{on}\\partial \\Omega, \\end{equation*} where $\\Delta_{p}$ is the $p$-Laplacian ($p>1$)$,$ and we emphasize the case $H(x,u,\\nabla u)=\\pm \\left\\| \\nabla u\\right\\| ^{q}$ ($q>0$). We obtain an existence result under subcritical growth assumptions on $H,$ we give necessary conditions of existence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6542","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"}