{"paper":{"title":"Deterministic KPZ-type equations with nonlocal \"gradient terms\"","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelbadie Younes, Antonio J. Fern\\'andez, Boumediene Abdellaoui, Tommaso Leonori","submitted_at":"2022-03-22T11:11:12Z","abstract_excerpt":"The main goal of this paper is to prove existence and non-existence results for deterministic Kardar-Parisi-Zhang type equations involving non-local \"gradient terms\". More precisely, let $\\Omega \\subset \\mathbb{R}^N$, $N \\geq 2$, be a bounded domain with boundary $\\partial \\Omega$ of class $C^2$. For $s \\in (0,1)$, we consider problems of the form \\[ \\tag{KPZ} \\left\\{ \\begin{aligned} (-\\Delta)^s u & = \\mu(x) |\\mathbb{D}(u)|^q + \\lambda f(x), \\quad && \\mbox{ in } \\Omega,\\\\ u & = 0, && \\mbox{ in } \\mathbb{R}^N \\setminus \\Omega, \\end{aligned} \\right. \\] where $q > 1$ and $\\lambda > 0$ are real pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.11616","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/2203.11616/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"}