{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GXMK5ZJ3FJUOVMKNSYCE3ST7TT","short_pith_number":"pith:GXMK5ZJ3","schema_version":"1.0","canonical_sha256":"35d8aee53b2a68eab14d96044dca7f9cc010da33ffedb6ba82daf893080a53c4","source":{"kind":"arxiv","id":"1901.02409","version":1},"attestation_state":"computed","paper":{"title":"Regularity of stable solutions to quasilinear elliptic equations on Riemannian models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Marcos do \\'O, Rodrigo Clemente","submitted_at":"2019-01-08T17:10:34Z","abstract_excerpt":"We investigate the regularity of semi-stable, radially symmetric, and decreasing solutions for a class of quasilinear reaction-diffusion equations in the inhomogeneous context of Riemannian manifolds. We prove uniform boundedness, Lebesgue and Sobolev estimates for this class of solutions for equations involving the p-Laplace Beltrami operator and locally Lipschitz non-linearity. We emphasize that our results do not depend on the boundary conditions and the specific form of the non-linearities and metric. Moreover, as an application, we establish regularity of the extremal solutions for equati"},"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":"1901.02409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-08T17:10:34Z","cross_cats_sorted":[],"title_canon_sha256":"c2ee0a37cced9f95b2cae6bba03e94f60159b96c7e70c6f044d3d6446bf16051","abstract_canon_sha256":"6d4dc6cc669f970a3741fcc20f686ca7d7a49a20af92c3772c9cc05e8e5c6507"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:43.420147Z","signature_b64":"l1a9lQQvs1UZz6Z5ZE0GJWzVSMP1HW33JL6oM0gaSR1iy1SmH/nvQt6SkGu8yQw/HbmHuevTeIEBpZoGg5T1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35d8aee53b2a68eab14d96044dca7f9cc010da33ffedb6ba82daf893080a53c4","last_reissued_at":"2026-05-17T23:56:43.419765Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:43.419765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of stable solutions to quasilinear elliptic equations on Riemannian models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Marcos do \\'O, Rodrigo Clemente","submitted_at":"2019-01-08T17:10:34Z","abstract_excerpt":"We investigate the regularity of semi-stable, radially symmetric, and decreasing solutions for a class of quasilinear reaction-diffusion equations in the inhomogeneous context of Riemannian manifolds. We prove uniform boundedness, Lebesgue and Sobolev estimates for this class of solutions for equations involving the p-Laplace Beltrami operator and locally Lipschitz non-linearity. We emphasize that our results do not depend on the boundary conditions and the specific form of the non-linearities and metric. Moreover, as an application, we establish regularity of the extremal solutions for equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02409","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":"1901.02409","created_at":"2026-05-17T23:56:43.419821+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.02409v1","created_at":"2026-05-17T23:56:43.419821+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02409","created_at":"2026-05-17T23:56:43.419821+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXMK5ZJ3FJUO","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXMK5ZJ3FJUOVMKN","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXMK5ZJ3","created_at":"2026-05-18T12:33:18.533446+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/GXMK5ZJ3FJUOVMKNSYCE3ST7TT","json":"https://pith.science/pith/GXMK5ZJ3FJUOVMKNSYCE3ST7TT.json","graph_json":"https://pith.science/api/pith-number/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/graph.json","events_json":"https://pith.science/api/pith-number/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/events.json","paper":"https://pith.science/paper/GXMK5ZJ3"},"agent_actions":{"view_html":"https://pith.science/pith/GXMK5ZJ3FJUOVMKNSYCE3ST7TT","download_json":"https://pith.science/pith/GXMK5ZJ3FJUOVMKNSYCE3ST7TT.json","view_paper":"https://pith.science/paper/GXMK5ZJ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.02409&json=true","fetch_graph":"https://pith.science/api/pith-number/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/graph.json","fetch_events":"https://pith.science/api/pith-number/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/action/storage_attestation","attest_author":"https://pith.science/pith/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/action/author_attestation","sign_citation":"https://pith.science/pith/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/action/citation_signature","submit_replication":"https://pith.science/pith/GXMK5ZJ3FJUOVMKNSYCE3ST7TT/action/replication_record"}},"created_at":"2026-05-17T23:56:43.419821+00:00","updated_at":"2026-05-17T23:56:43.419821+00:00"}