{"paper":{"title":"The Landis Conjecture For Nonlocal Elliptic Operators: Polynomial Decay","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gabrielle Nornberg, Sebasti\\'an Flores Sep\\'ulveda","submitted_at":"2025-01-01T22:27:48Z","abstract_excerpt":"We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2s which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption $o(|x|^{-(N+2s)})$ at infinity. Our result is new even in the case of the fractional Laplacian, as it unveils the nonlocal nature of the decay in Landis conjecture, evolving from exponential to polynomial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00969","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/2501.00969/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"}