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Precisely, let $M^-_{\\lambda, \\Lambda}$ be the Pucci's inf- operator, defined as the infimum of all linear uniformly elliptic operators with ellipticity constants $\\Lambda \\geq \\lambda >0$. Then, we prove that the inequality $M^-_{\\lambda, \\Lambda}(D^2u) +u^p \\leq 0$ does not have any positive viscosity solution in a halfspace provided that $-1\\leq p \\leq (\\Lambda/\\lambda n+1)/(\\Lambda/\\lambda n-1)$, whereas positive solutions do exist if ei"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1111.1083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-04T10:20:37Z","cross_cats_sorted":[],"title_canon_sha256":"dc98e9ef93c0e1e19b33ea516688503036b205e2cabb31715a3b35f9acef002c","abstract_canon_sha256":"a60e29658f910a83ab7cf55394406e0c275db154cc84623706eddd378c16a8c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:56.504263Z","signature_b64":"qfJxja/B22/tBOPNJVF66sRGkE656703GZp1We1zF+FqFn5jOgBpoyqG4GixgvEzaJxYyyvyN9qF7M7OYzEhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2fd24bfc2ba87104160790311a98d967b2073e7bb796088d284f73d500a414b","last_reissued_at":"2026-05-18T04:06:56.503503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:56.503503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit subsolutions and a Liouville theorem for fully nonlinear uniformly elliptic inequalities in halfspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabiana Leoni","submitted_at":"2011-11-04T10:20:37Z","abstract_excerpt":"We prove a Liouville type theorem for arbitrarily growing positive viscosity supersolutions of fully nonlinear uniformly elliptic equations in halfspaces. Precisely, let $M^-_{\\lambda, \\Lambda}$ be the Pucci's inf- operator, defined as the infimum of all linear uniformly elliptic operators with ellipticity constants $\\Lambda \\geq \\lambda >0$. Then, we prove that the inequality $M^-_{\\lambda, \\Lambda}(D^2u) +u^p \\leq 0$ does not have any positive viscosity solution in a halfspace provided that $-1\\leq p \\leq (\\Lambda/\\lambda n+1)/(\\Lambda/\\lambda n-1)$, whereas positive solutions do exist if ei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1083","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.1083","created_at":"2026-05-18T04:06:56.503637+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.1083v2","created_at":"2026-05-18T04:06:56.503637+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1083","created_at":"2026-05-18T04:06:56.503637+00:00"},{"alias_kind":"pith_short_12","alias_value":"UL6SJP6CXKDR","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UL6SJP6CXKDRAQLA","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UL6SJP6C","created_at":"2026-05-18T12:26:42.757692+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ","json":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ.json","graph_json":"https://pith.science/api/pith-number/UL6SJP6CXKDRAQLAPEBRDKMNSZ/graph.json","events_json":"https://pith.science/api/pith-number/UL6SJP6CXKDRAQLAPEBRDKMNSZ/events.json","paper":"https://pith.science/paper/UL6SJP6C"},"agent_actions":{"view_html":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ","download_json":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ.json","view_paper":"https://pith.science/paper/UL6SJP6C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.1083&json=true","fetch_graph":"https://pith.science/api/pith-number/UL6SJP6CXKDRAQLAPEBRDKMNSZ/graph.json","fetch_events":"https://pith.science/api/pith-number/UL6SJP6CXKDRAQLAPEBRDKMNSZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ/action/storage_attestation","attest_author":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ/action/author_attestation","sign_citation":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ/action/citation_signature","submit_replication":"https://pith.science/pith/UL6SJP6CXKDRAQLAPEBRDKMNSZ/action/replication_record"}},"created_at":"2026-05-18T04:06:56.503637+00:00","updated_at":"2026-05-18T04:06:56.503637+00:00"}