{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:3OAWXK4UWFGTRXKVMEKYYOO4IQ","short_pith_number":"pith:3OAWXK4U","schema_version":"1.0","canonical_sha256":"db816bab94b14d38dd5561158c39dc44007c653fbcf35bf72ac27db27c105958","source":{"kind":"arxiv","id":"1102.1924","version":1},"attestation_state":"computed","paper":{"title":"Sharp Moser-Trudinger inequalities for the Laplacian without boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carlo Morpurgo, Luigi Fontana","submitted_at":"2011-02-09T18:13:16Z","abstract_excerpt":"We derive a sharp Moser-Trudinger inequality for the borderline Sobolev imbedding of W^{2,n/2}(B_n) into the exponential class, where B_n is the unit ball of R^n. The corresponding sharp results for the spaces W_0^{d,n/d}(\\Omega) are well known, for general domains \\Omega, and are due to Moser and Adams. When the zero boundary condition is removed the only known results are for d=1 and are due to Chang-Yang, Cianchi and Leckband. Our proof is based on general abstract results recently obtained by the authors, and on a new integral representation formula for the \"canonical\" solution of the Pois"},"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":"1102.1924","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-02-09T18:13:16Z","cross_cats_sorted":[],"title_canon_sha256":"bd551cb0d2f65fab3aeedf1aaea2e1edff9ac64586e3c9107dd2cdea90eb423f","abstract_canon_sha256":"250322c36e64ee40b549036cf449b383cf0534b5c71619f91c675abba9947952"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:29:44.007802Z","signature_b64":"o6h8AxT1kIiOIUTAzH4ligwGUk8faRKiVMR5hQqgP+wgL3vZL1ALjA5K9igfaMvCS2PfJj11NmAZ8Q1muydaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db816bab94b14d38dd5561158c39dc44007c653fbcf35bf72ac27db27c105958","last_reissued_at":"2026-05-18T04:29:44.007398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:29:44.007398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Moser-Trudinger inequalities for the Laplacian without boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carlo Morpurgo, Luigi Fontana","submitted_at":"2011-02-09T18:13:16Z","abstract_excerpt":"We derive a sharp Moser-Trudinger inequality for the borderline Sobolev imbedding of W^{2,n/2}(B_n) into the exponential class, where B_n is the unit ball of R^n. The corresponding sharp results for the spaces W_0^{d,n/d}(\\Omega) are well known, for general domains \\Omega, and are due to Moser and Adams. When the zero boundary condition is removed the only known results are for d=1 and are due to Chang-Yang, Cianchi and Leckband. Our proof is based on general abstract results recently obtained by the authors, and on a new integral representation formula for the \"canonical\" solution of the Pois"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1924","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":"1102.1924","created_at":"2026-05-18T04:29:44.007462+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.1924v1","created_at":"2026-05-18T04:29:44.007462+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1924","created_at":"2026-05-18T04:29:44.007462+00:00"},{"alias_kind":"pith_short_12","alias_value":"3OAWXK4UWFGT","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"3OAWXK4UWFGTRXKV","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"3OAWXK4U","created_at":"2026-05-18T12:26:18.847500+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/3OAWXK4UWFGTRXKVMEKYYOO4IQ","json":"https://pith.science/pith/3OAWXK4UWFGTRXKVMEKYYOO4IQ.json","graph_json":"https://pith.science/api/pith-number/3OAWXK4UWFGTRXKVMEKYYOO4IQ/graph.json","events_json":"https://pith.science/api/pith-number/3OAWXK4UWFGTRXKVMEKYYOO4IQ/events.json","paper":"https://pith.science/paper/3OAWXK4U"},"agent_actions":{"view_html":"https://pith.science/pith/3OAWXK4UWFGTRXKVMEKYYOO4IQ","download_json":"https://pith.science/pith/3OAWXK4UWFGTRXKVMEKYYOO4IQ.json","view_paper":"https://pith.science/paper/3OAWXK4U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.1924&json=true","fetch_graph":"https://pith.science/api/pith-number/3OAWXK4UWFGTRXKVMEKYYOO4IQ/graph.json","fetch_events":"https://pith.science/api/pith-number/3OAWXK4UWFGTRXKVMEKYYOO4IQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3OAWXK4UWFGTRXKVMEKYYOO4IQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3OAWXK4UWFGTRXKVMEKYYOO4IQ/action/storage_attestation","attest_author":"https://pith.science/pith/3OAWXK4UWFGTRXKVMEKYYOO4IQ/action/author_attestation","sign_citation":"https://pith.science/pith/3OAWXK4UWFGTRXKVMEKYYOO4IQ/action/citation_signature","submit_replication":"https://pith.science/pith/3OAWXK4UWFGTRXKVMEKYYOO4IQ/action/replication_record"}},"created_at":"2026-05-18T04:29:44.007462+00:00","updated_at":"2026-05-18T04:29:44.007462+00:00"}