{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NWCUGVGKYLZEP6DPS2GJMBBH6O","short_pith_number":"pith:NWCUGVGK","schema_version":"1.0","canonical_sha256":"6d854354cac2f247f86f968c960427f3962ea1fe73c190765ec6187db2f04d08","source":{"kind":"arxiv","id":"1105.2545","version":1},"attestation_state":"computed","paper":{"title":"Schwarz Symmetrization and Comparison Results for Nonlinear Elliptic Equations and Eigenvalue Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e F\\'abio Bezerra Montenegro, Leonardo Prange Bonorino","submitted_at":"2011-05-12T18:33:03Z","abstract_excerpt":"We compare the distribution function and the maximum of solutions of nonlinear elliptic equations defined in general domains with solutions of similar problems defined in a ball using Schwarz symmetrization. As an application, we prove the existence and bound of solutions for some nonlinear equation. Moreover, for some nonlinear problems, we show that if the first $p$-eigenvalue of a domain is big, the supremum of a solution related to this domain is close to zero. For that we obtain $L^{\\infty}$ estimates for solutions of nonlinear and eigenvalue problems in terms of other $L^p$ norms."},"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":"1105.2545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-12T18:33:03Z","cross_cats_sorted":[],"title_canon_sha256":"7882ee3929873ad7e90a811e23400ad97ae7000111f51c74cd4253ce3f6b8c79","abstract_canon_sha256":"407ddad8e5884844d9400fc53dc394bffcd431eb0dc7ce1c9f496c38d11f349d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:54:11.262593Z","signature_b64":"8ph0l8d9S0KEkoMyhVBTVmrHYguojuNfDMhm9RZONRb+bs7dX5bzy1Nr6c1ARUcJEQYhArDTeZcCHBtkXQ3tCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d854354cac2f247f86f968c960427f3962ea1fe73c190765ec6187db2f04d08","last_reissued_at":"2026-07-05T02:54:11.262185Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:54:11.262185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schwarz Symmetrization and Comparison Results for Nonlinear Elliptic Equations and Eigenvalue Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e F\\'abio Bezerra Montenegro, Leonardo Prange Bonorino","submitted_at":"2011-05-12T18:33:03Z","abstract_excerpt":"We compare the distribution function and the maximum of solutions of nonlinear elliptic equations defined in general domains with solutions of similar problems defined in a ball using Schwarz symmetrization. As an application, we prove the existence and bound of solutions for some nonlinear equation. Moreover, for some nonlinear problems, we show that if the first $p$-eigenvalue of a domain is big, the supremum of a solution related to this domain is close to zero. For that we obtain $L^{\\infty}$ estimates for solutions of nonlinear and eigenvalue problems in terms of other $L^p$ norms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2545","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/1105.2545/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.2545","created_at":"2026-07-05T02:54:11.262258+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.2545v1","created_at":"2026-07-05T02:54:11.262258+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2545","created_at":"2026-07-05T02:54:11.262258+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWCUGVGKYLZE","created_at":"2026-07-05T02:54:11.262258+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWCUGVGKYLZEP6DP","created_at":"2026-07-05T02:54:11.262258+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWCUGVGK","created_at":"2026-07-05T02:54:11.262258+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/NWCUGVGKYLZEP6DPS2GJMBBH6O","json":"https://pith.science/pith/NWCUGVGKYLZEP6DPS2GJMBBH6O.json","graph_json":"https://pith.science/api/pith-number/NWCUGVGKYLZEP6DPS2GJMBBH6O/graph.json","events_json":"https://pith.science/api/pith-number/NWCUGVGKYLZEP6DPS2GJMBBH6O/events.json","paper":"https://pith.science/paper/NWCUGVGK"},"agent_actions":{"view_html":"https://pith.science/pith/NWCUGVGKYLZEP6DPS2GJMBBH6O","download_json":"https://pith.science/pith/NWCUGVGKYLZEP6DPS2GJMBBH6O.json","view_paper":"https://pith.science/paper/NWCUGVGK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.2545&json=true","fetch_graph":"https://pith.science/api/pith-number/NWCUGVGKYLZEP6DPS2GJMBBH6O/graph.json","fetch_events":"https://pith.science/api/pith-number/NWCUGVGKYLZEP6DPS2GJMBBH6O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWCUGVGKYLZEP6DPS2GJMBBH6O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWCUGVGKYLZEP6DPS2GJMBBH6O/action/storage_attestation","attest_author":"https://pith.science/pith/NWCUGVGKYLZEP6DPS2GJMBBH6O/action/author_attestation","sign_citation":"https://pith.science/pith/NWCUGVGKYLZEP6DPS2GJMBBH6O/action/citation_signature","submit_replication":"https://pith.science/pith/NWCUGVGKYLZEP6DPS2GJMBBH6O/action/replication_record"}},"created_at":"2026-07-05T02:54:11.262258+00:00","updated_at":"2026-07-05T02:54:11.262258+00:00"}