{"paper":{"title":"Uniqueness of solutions to an elliptic inequality with rapid decay at infinity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"F. Golgeleyen, M. Yamamoto, O.Y. Imanuvilov","submitted_at":"2025-05-20T14:39:24Z","abstract_excerpt":"We consider an elliptic differential inequality: $\\vert \\Delta u(x) \\vert \\le C_0(\\YYYY^{-\\gamma}\\vert u(x)\\vert + \\YYYY^{-\\theta}\\vert \\nabla u(x)\\vert)$ in an exterior domain $\\R^n \\setminus \\ooo{U}$, where $U$ is a simply connected bounded domain $U$, $x := (y,z) \\in \\R^n$ with $y \\in \\R^m$ and $z\\in \\R^{n-m}$ for given $m\\in \\{ 1, ..., n\\}$, and $\\gamma, \\theta \\in \\R$ are constants. We assume that $u(x)$ decays with exponential rate in the $y$-coordinates and polynomial rate in the $z$-coordinates as $\\vert x\\vert \\to \\infty$. We prove that if decay rates of $u$ satisfy certain conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14431","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/2505.14431/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"}