{"paper":{"title":"Anisotropic elliptic equations with gradient-dependent lower order terms and $L^1$ data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Brandolini, Florica C. C\\^irstea","submitted_at":"2020-01-08T21:49:56Z","abstract_excerpt":"We prove the existence of a weak solution for a general class of Dirichlet anisotropic elliptic problems such as $\\mathcal Au+\\Phi(x,u,\\nabla u)=\\mathfrak{B}u+f$ in $\\Omega$, where $\\Omega$ is a bounded open subset of $\\mathbb R^N$ and $f\\in L^1(\\Omega)$ is arbitrary. The principal part is a divergence-form nonlinear anisotropic operator $\\mathcal A$, the prototype of which is $\\mathcal A u=-\\sum_{j=1}^N \\partial_j(|\\partial_j u|^{p_j-2}\\partial_j u)$ with $p_j>1$ for all $1\\leq j\\leq N$ and $\\sum_{j=1}^N (1/p_j)>1$. As a novelty in this paper, our lower order terms involve a new class of oper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.02754","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.02754/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}