{"paper":{"title":"Gradient bounds for a widely degenerate orthotropic parabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pasquale Ambrosio","submitted_at":"2025-11-03T11:42:56Z","abstract_excerpt":"In this paper, we consider the following nonlinear parabolic equation \\[ \\partial_{t}u\\,=\\,\\sum_{i=1}^{n}\\partial_{x_{i}}\\left[(\\vert u_{x_{i}}\\vert-\\delta_{i})_{+}^{p-1}\\frac{u_{x_{i}}}{\\vert u_{x_{i}}\\vert}\\right]\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\mathrm{in}\\,\\,\\,\\Omega\\times I, \\] where $\\Omega$ is a bounded open subset of $\\mathbb{R}^{n}$ for $n\\geq2$, $I\\subset\\mathbb{R}$ is a bounded open interval, $p\\geq2$, $\\delta_{1},\\ldots,\\delta_{n}$ are non-negative numbers and $\\left(\\,\\cdot\\,\\right)_{+}$ denotes the positive part. We prove that the local weak solutions are locally Lipschitz continuous in the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.01480","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.01480/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"}