{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BAB6TPVPVVR5MY3X6DF3R4ZLCH","short_pith_number":"pith:BAB6TPVP","schema_version":"1.0","canonical_sha256":"0803e9beafad63d66377f0cbb8f32b11e3be53a09349457d53c7027d81ff474e","source":{"kind":"arxiv","id":"1712.10208","version":1},"attestation_state":"computed","paper":{"title":"On the best constant for Gagliardo-Nirenberg interpolation inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jian-Guo Liu, Jinhuan Wang","submitted_at":"2017-12-29T12:58:04Z","abstract_excerpt":"In this paper we derive the best constant for the following Gagliardo-Nirenberg interpolation inequality\n  \\begin{eqnarray*} \\|u\\|_{L^{m+1}}\\leq C_{q,m,p} \\|u\\|^{1-\\theta}_{L^{q+1}}\\|\\nabla u\\|^{\\theta}_{L^p},\\quad \\theta=\\frac{pd(m-q)}{(m+1)[d(p-q-1)+p(q+1)]}, \\end{eqnarray*} where parameters $q,m,p$ respectively belong to the following two ranges:\n  (i) $p>d\\geq 1$, $q\\geq0$ and $m=\\infty$. That shows $L^{\\infty}$-type Gagliardo-Nirenberg interpolation inequality.\n  (ii) $p>\\max\\{1,\\frac{2d}{d+2}\\}$, $0\\leq q<\\sigma-1$, and $q<m<\\sigma$, where $\\sigma$ is defined by $ \\sigma:= \\frac{(p-1)d+p"},"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":"1712.10208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-29T12:58:04Z","cross_cats_sorted":[],"title_canon_sha256":"4ef768c8d803321e21382bafaab20f64dcdf1a3c03837c2bf0c44221818fb126","abstract_canon_sha256":"57e1578871e73529a9893be1d12a4689a8a281fee3dfc02c29123a31561c8be9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:03.700164Z","signature_b64":"tGL5bRqX+uwUtq9jsS4ZfrIf6LcTVeJY7xdiRVmPUO+gAUcs/K8VmZiILDlv0t3bTypfRalh4MqZMnWKGZvfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0803e9beafad63d66377f0cbb8f32b11e3be53a09349457d53c7027d81ff474e","last_reissued_at":"2026-05-18T00:27:03.699620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:03.699620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the best constant for Gagliardo-Nirenberg interpolation inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jian-Guo Liu, Jinhuan Wang","submitted_at":"2017-12-29T12:58:04Z","abstract_excerpt":"In this paper we derive the best constant for the following Gagliardo-Nirenberg interpolation inequality\n  \\begin{eqnarray*} \\|u\\|_{L^{m+1}}\\leq C_{q,m,p} \\|u\\|^{1-\\theta}_{L^{q+1}}\\|\\nabla u\\|^{\\theta}_{L^p},\\quad \\theta=\\frac{pd(m-q)}{(m+1)[d(p-q-1)+p(q+1)]}, \\end{eqnarray*} where parameters $q,m,p$ respectively belong to the following two ranges:\n  (i) $p>d\\geq 1$, $q\\geq0$ and $m=\\infty$. That shows $L^{\\infty}$-type Gagliardo-Nirenberg interpolation inequality.\n  (ii) $p>\\max\\{1,\\frac{2d}{d+2}\\}$, $0\\leq q<\\sigma-1$, and $q<m<\\sigma$, where $\\sigma$ is defined by $ \\sigma:= \\frac{(p-1)d+p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10208","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":"1712.10208","created_at":"2026-05-18T00:27:03.699697+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.10208v1","created_at":"2026-05-18T00:27:03.699697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.10208","created_at":"2026-05-18T00:27:03.699697+00:00"},{"alias_kind":"pith_short_12","alias_value":"BAB6TPVPVVR5","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BAB6TPVPVVR5MY3X","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BAB6TPVP","created_at":"2026-05-18T12:31:08.081275+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/BAB6TPVPVVR5MY3X6DF3R4ZLCH","json":"https://pith.science/pith/BAB6TPVPVVR5MY3X6DF3R4ZLCH.json","graph_json":"https://pith.science/api/pith-number/BAB6TPVPVVR5MY3X6DF3R4ZLCH/graph.json","events_json":"https://pith.science/api/pith-number/BAB6TPVPVVR5MY3X6DF3R4ZLCH/events.json","paper":"https://pith.science/paper/BAB6TPVP"},"agent_actions":{"view_html":"https://pith.science/pith/BAB6TPVPVVR5MY3X6DF3R4ZLCH","download_json":"https://pith.science/pith/BAB6TPVPVVR5MY3X6DF3R4ZLCH.json","view_paper":"https://pith.science/paper/BAB6TPVP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.10208&json=true","fetch_graph":"https://pith.science/api/pith-number/BAB6TPVPVVR5MY3X6DF3R4ZLCH/graph.json","fetch_events":"https://pith.science/api/pith-number/BAB6TPVPVVR5MY3X6DF3R4ZLCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BAB6TPVPVVR5MY3X6DF3R4ZLCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BAB6TPVPVVR5MY3X6DF3R4ZLCH/action/storage_attestation","attest_author":"https://pith.science/pith/BAB6TPVPVVR5MY3X6DF3R4ZLCH/action/author_attestation","sign_citation":"https://pith.science/pith/BAB6TPVPVVR5MY3X6DF3R4ZLCH/action/citation_signature","submit_replication":"https://pith.science/pith/BAB6TPVPVVR5MY3X6DF3R4ZLCH/action/replication_record"}},"created_at":"2026-05-18T00:27:03.699697+00:00","updated_at":"2026-05-18T00:27:03.699697+00:00"}