{"paper":{"title":"Monotonicity of non-negative solutions of quasilinear elliptic equations in a cylindrical domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Berardino Sciunzi, Giuseppe Spadaro, Luigi Montoro, Luigi Muglia","submitted_at":"2026-07-01T08:37:31Z","abstract_excerpt":"We consider weak solutions to $p$-Laplace equations in cylindrical domains under mixed homogeneous Dirichlet-Neumann boundary conditions. We assume that the right-hand side is positive and locally Lipschitz continuous and we prove that any positive solution is monotone increasing in the $x_N$ direction for any $p>1$. As an application we prove that solutions to Allen-Cahn type equations are one-dimensional as well as a Liouville type result for Lane-Emden type equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00617","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/2607.00617/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"}