{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:T6CZ375UXIURIZSXHWGDI5DF3L","short_pith_number":"pith:T6CZ375U","schema_version":"1.0","canonical_sha256":"9f859dffb4ba291466573d8c347465dadc0a5b43e2afae91810a8dd48cedc8ca","source":{"kind":"arxiv","id":"1908.01331","version":1},"attestation_state":"computed","paper":{"title":"Energy asymptotics in the three-dimensional Brezis--Nirenberg problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hynek Kovarik, Rupert L. Frank, Tobias K\\\"onig","submitted_at":"2019-08-04T12:43:12Z","abstract_excerpt":"For a bounded open set $\\Omega\\subset\\mathbb R^3$ we consider the minimization problem $$ S(a+\\epsilon V) = \\inf_{0\\not\\equiv u\\in H^1_0(\\Omega)} \\frac{\\int_\\Omega (|\\nabla u|^2+ (a+\\epsilon V) |u|^2)\\,dx}{(\\int_\\Omega u^6\\,dx)^{1/3}} $$ involving the critical Sobolev exponent. The function $a$ is assumed to be critical in the sense of Hebey and Vaugon. Under certain assumptions on $a$ and $V$ we compute the asymptotics of $S(a+\\epsilon V)-S$ as $\\epsilon\\to 0+$, where $S$ is the Sobolev constant. (Almost) minimizers concentrate at a point in the zero set of the Robin function corresponding to"},"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":"1908.01331","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-04T12:43:12Z","cross_cats_sorted":[],"title_canon_sha256":"4c44fe0f7e69fc2ad7d181df0382a34928647738b2004c2544fe0181ba835465","abstract_canon_sha256":"ab976f033ff7905381eb6bc93dbf7a3dd43064e6896cce3e1806f12306075317"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:26:10.418214Z","signature_b64":"dvKRKR4MP12JcnXCn9N/nrI6JrJB4LVNx6Z8L2iKZtLdWhdq+yJR5jbtfiGAWTGk7BGUF+v702rj4ctav114Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f859dffb4ba291466573d8c347465dadc0a5b43e2afae91810a8dd48cedc8ca","last_reissued_at":"2026-07-05T02:26:10.417811Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:26:10.417811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy asymptotics in the three-dimensional Brezis--Nirenberg problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hynek Kovarik, Rupert L. Frank, Tobias K\\\"onig","submitted_at":"2019-08-04T12:43:12Z","abstract_excerpt":"For a bounded open set $\\Omega\\subset\\mathbb R^3$ we consider the minimization problem $$ S(a+\\epsilon V) = \\inf_{0\\not\\equiv u\\in H^1_0(\\Omega)} \\frac{\\int_\\Omega (|\\nabla u|^2+ (a+\\epsilon V) |u|^2)\\,dx}{(\\int_\\Omega u^6\\,dx)^{1/3}} $$ involving the critical Sobolev exponent. The function $a$ is assumed to be critical in the sense of Hebey and Vaugon. Under certain assumptions on $a$ and $V$ we compute the asymptotics of $S(a+\\epsilon V)-S$ as $\\epsilon\\to 0+$, where $S$ is the Sobolev constant. (Almost) minimizers concentrate at a point in the zero set of the Robin function corresponding to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01331","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/1908.01331/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":"1908.01331","created_at":"2026-07-05T02:26:10.417871+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.01331v1","created_at":"2026-07-05T02:26:10.417871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01331","created_at":"2026-07-05T02:26:10.417871+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6CZ375UXIUR","created_at":"2026-07-05T02:26:10.417871+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6CZ375UXIURIZSX","created_at":"2026-07-05T02:26:10.417871+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6CZ375U","created_at":"2026-07-05T02:26:10.417871+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/T6CZ375UXIURIZSXHWGDI5DF3L","json":"https://pith.science/pith/T6CZ375UXIURIZSXHWGDI5DF3L.json","graph_json":"https://pith.science/api/pith-number/T6CZ375UXIURIZSXHWGDI5DF3L/graph.json","events_json":"https://pith.science/api/pith-number/T6CZ375UXIURIZSXHWGDI5DF3L/events.json","paper":"https://pith.science/paper/T6CZ375U"},"agent_actions":{"view_html":"https://pith.science/pith/T6CZ375UXIURIZSXHWGDI5DF3L","download_json":"https://pith.science/pith/T6CZ375UXIURIZSXHWGDI5DF3L.json","view_paper":"https://pith.science/paper/T6CZ375U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.01331&json=true","fetch_graph":"https://pith.science/api/pith-number/T6CZ375UXIURIZSXHWGDI5DF3L/graph.json","fetch_events":"https://pith.science/api/pith-number/T6CZ375UXIURIZSXHWGDI5DF3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6CZ375UXIURIZSXHWGDI5DF3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6CZ375UXIURIZSXHWGDI5DF3L/action/storage_attestation","attest_author":"https://pith.science/pith/T6CZ375UXIURIZSXHWGDI5DF3L/action/author_attestation","sign_citation":"https://pith.science/pith/T6CZ375UXIURIZSXHWGDI5DF3L/action/citation_signature","submit_replication":"https://pith.science/pith/T6CZ375UXIURIZSXHWGDI5DF3L/action/replication_record"}},"created_at":"2026-07-05T02:26:10.417871+00:00","updated_at":"2026-07-05T02:26:10.417871+00:00"}