{"paper":{"title":"A note on the $L^{p}$-solvability of a strongly-coupled nonlocal system of equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miriam Abbate, Tadele Mengesha","submitted_at":"2025-11-25T19:07:50Z","abstract_excerpt":"The goal of this paper is to study the $L^p$-solvability of the strongly-coupled nonlocal system \\[\n  \\mathbb{L} \\mathbf{u} (\\mathbf{x}) + \\lambda \\mathbf{u}(\\mathbf{x})= \\mathbf{f}(\\mathbf{x}) \\quad \\text{in $\\mathbb{R}^{d}$ } \\] where $\\mathbb{L}$ is a linear nonlocal coupled vector-valued operator associated with a kernel $K$ comparable to $|\\mathbf{y}|^{-(d+2s)}$ for $s \\in (0,1)$, satisfying certain ellipticity and cancellation conditions. For any $\\mathbf{f} \\in [L^p(\\mathbb{R}^d)]^d$, $1< p < \\infty$, the existence of a unique strong solution $\\mathbf{u} \\in [H^{2s,p}(\\mathbb{R}^d)]^d$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.20772","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/2511.20772/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"}