{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:XFLAMGN6OCP5AKVRVZTYNDLWYJ","short_pith_number":"pith:XFLAMGN6","schema_version":"1.0","canonical_sha256":"b9560619be709fd02ab1ae67868d76c26d565e7d28c79e8ecfab2aef0e77b841","source":{"kind":"arxiv","id":"1412.1277","version":1},"attestation_state":"computed","paper":{"title":"Sharp estimates of radial minimizers of p-Laplace equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miguel Angel Navarro, Salvador Villegas","submitted_at":"2014-12-03T11:25:15Z","abstract_excerpt":"In this paper we study semi-stable, radially symmetric and decreasing solutions $u\\in W^{1,p}(B_1)$ of $-\\Delta_p u=g(u)$ in $B_1\\setminus\\{0\\}$, where $B_1$ is the unit ball of $\\mathbb{R}^N$, $p>1$, $\\Delta_p$ is the $p-$Laplace operator and $g$ is a general locally Lipschitz function. We establish sharp pointwise estimates for such solutions. As an application of these results, we obtain optimal pointwise estimates for the extremal solution and its derivatives (up to order three) of the equation $-\\Delta_p u=\\lambda f(u)$, posed in $B_1$, with Dirichlet data $u|_{\\partial B_1}=0$, where the"},"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":"1412.1277","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-03T11:25:15Z","cross_cats_sorted":[],"title_canon_sha256":"a9a278d850b831d34cfd8b17c3f459f33a621163af1162e27b5f203c6fa4c7bf","abstract_canon_sha256":"3b93ed53f10470cb8b8aae0e5ccd660f0bb12de663051524e4a33d275fd076cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:12.933332Z","signature_b64":"hQ418sEs4vgrUee00NA3/O3IxBQVNZSbypWGVZ/0kDEH9krO46VHZTCwAV+bdtGnpIqt5l2fFo08Hn5D56C/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9560619be709fd02ab1ae67868d76c26d565e7d28c79e8ecfab2aef0e77b841","last_reissued_at":"2026-05-18T02:32:12.932773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:12.932773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp estimates of radial minimizers of p-Laplace equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miguel Angel Navarro, Salvador Villegas","submitted_at":"2014-12-03T11:25:15Z","abstract_excerpt":"In this paper we study semi-stable, radially symmetric and decreasing solutions $u\\in W^{1,p}(B_1)$ of $-\\Delta_p u=g(u)$ in $B_1\\setminus\\{0\\}$, where $B_1$ is the unit ball of $\\mathbb{R}^N$, $p>1$, $\\Delta_p$ is the $p-$Laplace operator and $g$ is a general locally Lipschitz function. We establish sharp pointwise estimates for such solutions. As an application of these results, we obtain optimal pointwise estimates for the extremal solution and its derivatives (up to order three) of the equation $-\\Delta_p u=\\lambda f(u)$, posed in $B_1$, with Dirichlet data $u|_{\\partial B_1}=0$, where the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1277","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":"1412.1277","created_at":"2026-05-18T02:32:12.932877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1277v1","created_at":"2026-05-18T02:32:12.932877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1277","created_at":"2026-05-18T02:32:12.932877+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFLAMGN6OCP5","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFLAMGN6OCP5AKVR","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFLAMGN6","created_at":"2026-05-18T12:28:57.508820+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/XFLAMGN6OCP5AKVRVZTYNDLWYJ","json":"https://pith.science/pith/XFLAMGN6OCP5AKVRVZTYNDLWYJ.json","graph_json":"https://pith.science/api/pith-number/XFLAMGN6OCP5AKVRVZTYNDLWYJ/graph.json","events_json":"https://pith.science/api/pith-number/XFLAMGN6OCP5AKVRVZTYNDLWYJ/events.json","paper":"https://pith.science/paper/XFLAMGN6"},"agent_actions":{"view_html":"https://pith.science/pith/XFLAMGN6OCP5AKVRVZTYNDLWYJ","download_json":"https://pith.science/pith/XFLAMGN6OCP5AKVRVZTYNDLWYJ.json","view_paper":"https://pith.science/paper/XFLAMGN6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1277&json=true","fetch_graph":"https://pith.science/api/pith-number/XFLAMGN6OCP5AKVRVZTYNDLWYJ/graph.json","fetch_events":"https://pith.science/api/pith-number/XFLAMGN6OCP5AKVRVZTYNDLWYJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFLAMGN6OCP5AKVRVZTYNDLWYJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFLAMGN6OCP5AKVRVZTYNDLWYJ/action/storage_attestation","attest_author":"https://pith.science/pith/XFLAMGN6OCP5AKVRVZTYNDLWYJ/action/author_attestation","sign_citation":"https://pith.science/pith/XFLAMGN6OCP5AKVRVZTYNDLWYJ/action/citation_signature","submit_replication":"https://pith.science/pith/XFLAMGN6OCP5AKVRVZTYNDLWYJ/action/replication_record"}},"created_at":"2026-05-18T02:32:12.932877+00:00","updated_at":"2026-05-18T02:32:12.932877+00:00"}