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We establish that $\\log (\\vp)$ is concave in the case $p=1$ and that the function $\\vp^{\\frac{1-p}{2}}$ is"},"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":"1202.0218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-01T17:06:07Z","cross_cats_sorted":[],"title_canon_sha256":"6807d26213cc2b839745dee9ad638b797217f2eb9844ff9b492d55c648982d39","abstract_canon_sha256":"cf5385bfb5a21c5c84ba09441df7ecb5e8025dc88ba0542d10442620426f870a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:19.861558Z","signature_b64":"V8wIuzBzio5vKdFf6Kt/AIf26YugyCwPG75Im4aDTkGCpH+K7o8vh6dRx0UcT4wZtmTu6wVnTDYXHCIrzGWaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ef2b9fb8034a863048bb8fd6a144d35f8cf439d43d9edf059f72b3579fa60cc","last_reissued_at":"2026-05-18T04:03:19.861010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:19.861010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic Behavior in Degenerate Parabolic Fully Nonlinear equations and its application to Elliptic Eigenvalue Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ki-Ahm Lee, Soojung Kim","submitted_at":"2012-02-01T17:06:07Z","abstract_excerpt":"We study the asymptotic behavior of the nonlinear parabolic flows $u_{t}=F(D^2 u^m)$ when $t\\ra \\infty$ for $m\\geq 1$, and the geometric properties for solutions of the following elliptic nonlinear eigenvalue problems:\n  F(D^2 \\vp) &+ \\mu\\vp^{p}=0, \\quad \\vp>0\\quad\\text{in $\\Omega$}\n  \\vp&=0\\quad\\text{on $\\p\\Omega$}\nposed in a (strictly) convex and smooth domain $\\Omega\\subset\\re^n$ for $0< p \\leq 1,$ where $F(\\cdot)$ is uniformly elliptic, positively homogeneous of order one and concave. We establish that $\\log (\\vp)$ is concave in the case $p=1$ and that the function $\\vp^{\\frac{1-p}{2}}$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0218","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":""},"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":"1202.0218","created_at":"2026-05-18T04:03:19.861095+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.0218v1","created_at":"2026-05-18T04:03:19.861095+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0218","created_at":"2026-05-18T04:03:19.861095+00:00"},{"alias_kind":"pith_short_12","alias_value":"N3ZLT64AGSUG","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"N3ZLT64AGSUGGBEL","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"N3ZLT64A","created_at":"2026-05-18T12:27:16.716162+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/N3ZLT64AGSUGGBELXD6WUFCNGX","json":"https://pith.science/pith/N3ZLT64AGSUGGBELXD6WUFCNGX.json","graph_json":"https://pith.science/api/pith-number/N3ZLT64AGSUGGBELXD6WUFCNGX/graph.json","events_json":"https://pith.science/api/pith-number/N3ZLT64AGSUGGBELXD6WUFCNGX/events.json","paper":"https://pith.science/paper/N3ZLT64A"},"agent_actions":{"view_html":"https://pith.science/pith/N3ZLT64AGSUGGBELXD6WUFCNGX","download_json":"https://pith.science/pith/N3ZLT64AGSUGGBELXD6WUFCNGX.json","view_paper":"https://pith.science/paper/N3ZLT64A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.0218&json=true","fetch_graph":"https://pith.science/api/pith-number/N3ZLT64AGSUGGBELXD6WUFCNGX/graph.json","fetch_events":"https://pith.science/api/pith-number/N3ZLT64AGSUGGBELXD6WUFCNGX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N3ZLT64AGSUGGBELXD6WUFCNGX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N3ZLT64AGSUGGBELXD6WUFCNGX/action/storage_attestation","attest_author":"https://pith.science/pith/N3ZLT64AGSUGGBELXD6WUFCNGX/action/author_attestation","sign_citation":"https://pith.science/pith/N3ZLT64AGSUGGBELXD6WUFCNGX/action/citation_signature","submit_replication":"https://pith.science/pith/N3ZLT64AGSUGGBELXD6WUFCNGX/action/replication_record"}},"created_at":"2026-05-18T04:03:19.861095+00:00","updated_at":"2026-05-18T04:03:19.861095+00:00"}