{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:EDRPSWJHA7VALCRDUM6NJFZUJT","short_pith_number":"pith:EDRPSWJH","schema_version":"1.0","canonical_sha256":"20e2f9592707ea058a23a33cd497344cd4530179b15b40b0e7997baff25b9132","source":{"kind":"arxiv","id":"1603.01737","version":2},"attestation_state":"computed","paper":{"title":"On the $p$-Laplacian with Robin boundary conditions and boundary trace theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Hynek Kovarik, Konstantin Pankrashkin","submitted_at":"2016-03-05T15:42:33Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^\\nu$, $\\nu\\ge 2$, be a $C^{1,1}$ domain whose boundary $\\partial\\Omega$ is either compact or behaves suitably at infinity. For $p\\in(1,\\infty)$ and $\\alpha>0$, define \\[ \\Lambda(\\Omega,p,\\alpha):=\\inf_{\\substack{u\\in W^{1,p}(\\Omega)\\\\ u\\not\\equiv 0}}\\dfrac{\\displaystyle \\int_\\Omega |\\nabla u|^p \\mathrm{d} x - \\alpha\\displaystyle\\int_{\\partial\\Omega} |u|^p\\mathrm{d}\\sigma}{\\displaystyle\\int_\\Omega |u|^p\\mathrm{d} x}, \\] where $\\mathrm{d}\\sigma$ is the surface measure on $\\partial\\Omega$. We show the asymptotics \\[ \\Lambda(\\Omega,p,\\alpha)=-(p-1)\\alpha^{\\frac{p}{p-1}"},"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":"1603.01737","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-03-05T15:42:33Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b5e8e91cd62695dfa3769c56deaad0a66d14cd5101cd1d5945bbe22ff7f21894","abstract_canon_sha256":"dd307b31f61a167716d0a6727fcc54fba2920ba1b5e7dcd6db76946f5461c374"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:35.000339Z","signature_b64":"Y5MVR7+Il7/+xXrei1rB7Bikx3JGMbdG7e06ULBocTFMxn1QpoTvahNsp3Df9gpmPP6nDU1EVVYehaq7sUpXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20e2f9592707ea058a23a33cd497344cd4530179b15b40b0e7997baff25b9132","last_reissued_at":"2026-05-18T00:45:34.999861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:34.999861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $p$-Laplacian with Robin boundary conditions and boundary trace theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Hynek Kovarik, Konstantin Pankrashkin","submitted_at":"2016-03-05T15:42:33Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^\\nu$, $\\nu\\ge 2$, be a $C^{1,1}$ domain whose boundary $\\partial\\Omega$ is either compact or behaves suitably at infinity. For $p\\in(1,\\infty)$ and $\\alpha>0$, define \\[ \\Lambda(\\Omega,p,\\alpha):=\\inf_{\\substack{u\\in W^{1,p}(\\Omega)\\\\ u\\not\\equiv 0}}\\dfrac{\\displaystyle \\int_\\Omega |\\nabla u|^p \\mathrm{d} x - \\alpha\\displaystyle\\int_{\\partial\\Omega} |u|^p\\mathrm{d}\\sigma}{\\displaystyle\\int_\\Omega |u|^p\\mathrm{d} x}, \\] where $\\mathrm{d}\\sigma$ is the surface measure on $\\partial\\Omega$. We show the asymptotics \\[ \\Lambda(\\Omega,p,\\alpha)=-(p-1)\\alpha^{\\frac{p}{p-1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01737","kind":"arxiv","version":2},"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":"1603.01737","created_at":"2026-05-18T00:45:34.999942+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.01737v2","created_at":"2026-05-18T00:45:34.999942+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01737","created_at":"2026-05-18T00:45:34.999942+00:00"},{"alias_kind":"pith_short_12","alias_value":"EDRPSWJHA7VA","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"EDRPSWJHA7VALCRD","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"EDRPSWJH","created_at":"2026-05-18T12:30:12.583610+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/EDRPSWJHA7VALCRDUM6NJFZUJT","json":"https://pith.science/pith/EDRPSWJHA7VALCRDUM6NJFZUJT.json","graph_json":"https://pith.science/api/pith-number/EDRPSWJHA7VALCRDUM6NJFZUJT/graph.json","events_json":"https://pith.science/api/pith-number/EDRPSWJHA7VALCRDUM6NJFZUJT/events.json","paper":"https://pith.science/paper/EDRPSWJH"},"agent_actions":{"view_html":"https://pith.science/pith/EDRPSWJHA7VALCRDUM6NJFZUJT","download_json":"https://pith.science/pith/EDRPSWJHA7VALCRDUM6NJFZUJT.json","view_paper":"https://pith.science/paper/EDRPSWJH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.01737&json=true","fetch_graph":"https://pith.science/api/pith-number/EDRPSWJHA7VALCRDUM6NJFZUJT/graph.json","fetch_events":"https://pith.science/api/pith-number/EDRPSWJHA7VALCRDUM6NJFZUJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EDRPSWJHA7VALCRDUM6NJFZUJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EDRPSWJHA7VALCRDUM6NJFZUJT/action/storage_attestation","attest_author":"https://pith.science/pith/EDRPSWJHA7VALCRDUM6NJFZUJT/action/author_attestation","sign_citation":"https://pith.science/pith/EDRPSWJHA7VALCRDUM6NJFZUJT/action/citation_signature","submit_replication":"https://pith.science/pith/EDRPSWJHA7VALCRDUM6NJFZUJT/action/replication_record"}},"created_at":"2026-05-18T00:45:34.999942+00:00","updated_at":"2026-05-18T00:45:34.999942+00:00"}