{"paper":{"title":"Boundedness of solutions to singular anisotropic elliptic equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Brandolini, Florica Corina Cirstea","submitted_at":"2023-07-17T10:09:12Z","abstract_excerpt":"We prove the uniform boundedness of all solutions for a general class of Dirichlet anisotropic elliptic problems of the form $$-\\Delta_{\\overrightarrow{p}}u+\\Phi_0(u,\\nabla u)=\\Psi(u,\\nabla u) +f $$ on a bounded open subset $\\Omega\\subset \\mathbb R^N$ $(N\\geq 2)$, where $ \\Delta_{\\overrightarrow{p}}u=\\sum_{j=1}^N \\partial_j (|\\partial_j u|^{p_j-2}\\partial_j u)$ and $\\Phi_0(u,\\nabla u)=\\left(\\mathfrak{a}_0+\\sum_{j=1}^N \\mathfrak{a}_j |\\partial_j u|^{p_j}\\right)|u|^{m-2}u$, with $\\mathfrak{a}_0>0$, $m,p_j>1$, $\\mathfrak{a}_j\\geq 0$ for $1\\leq j\\leq N$ and $N/p=\\sum_{k=1}^N (1/p_k)>1$. We assume "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.08369","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.08369/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"}