{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DOMQG7QUADMLWKJ67M6B3OCCL3","short_pith_number":"pith:DOMQG7QU","schema_version":"1.0","canonical_sha256":"1b99037e1400d8bb293efb3c1db8425ec7f0d7e0943babd95eeee8d73431dda8","source":{"kind":"arxiv","id":"1802.01404","version":1},"attestation_state":"computed","paper":{"title":"Blowup Analysis for the Perfect Conductivity Problem with convex but not strictly convex inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haigang Li, Hongjie Ju, Longjuan Xu","submitted_at":"2018-02-05T14:21:56Z","abstract_excerpt":"In the perfect conductivity problem, it is interesting to study whether the electric field can become arbitrarily large or not, in a narrow region between two adjacent perfectly conducting inclusions. In this paper, we show that the relative convexity of two adjacent inclusions plays a key role in the blowup analysis of the electric field and find some new phenomena. By energy method, we prove the boundedness of the gradient of the solution if two adjacent inclusions fail to be locally relatively strictly convex, namely, if the top and bottom boundaries of the narrow region are partially \"flat"},"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":"1802.01404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-02-05T14:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"04704c3cc67865d1e7038d6848092889ebe49bd3af56cf3b506918a308f29f6c","abstract_canon_sha256":"7a0d9fe5131aeebf34739b90b69d4ea22230906f21a11be27ed893d0cfa4e97a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:26.475878Z","signature_b64":"FPhAfOuKkqamUZe6wSdWX3GYYWZ/DdzpF13vX8q94f1xDL2R2mYwgLVRmuVztCKOvsGtUq10miCJVqaA+rJHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b99037e1400d8bb293efb3c1db8425ec7f0d7e0943babd95eeee8d73431dda8","last_reissued_at":"2026-05-18T00:24:26.475395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:26.475395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blowup Analysis for the Perfect Conductivity Problem with convex but not strictly convex inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haigang Li, Hongjie Ju, Longjuan Xu","submitted_at":"2018-02-05T14:21:56Z","abstract_excerpt":"In the perfect conductivity problem, it is interesting to study whether the electric field can become arbitrarily large or not, in a narrow region between two adjacent perfectly conducting inclusions. In this paper, we show that the relative convexity of two adjacent inclusions plays a key role in the blowup analysis of the electric field and find some new phenomena. By energy method, we prove the boundedness of the gradient of the solution if two adjacent inclusions fail to be locally relatively strictly convex, namely, if the top and bottom boundaries of the narrow region are partially \"flat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01404","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":"1802.01404","created_at":"2026-05-18T00:24:26.475470+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.01404v1","created_at":"2026-05-18T00:24:26.475470+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01404","created_at":"2026-05-18T00:24:26.475470+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOMQG7QUADML","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOMQG7QUADMLWKJ6","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOMQG7QU","created_at":"2026-05-18T12:32:19.392346+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/DOMQG7QUADMLWKJ67M6B3OCCL3","json":"https://pith.science/pith/DOMQG7QUADMLWKJ67M6B3OCCL3.json","graph_json":"https://pith.science/api/pith-number/DOMQG7QUADMLWKJ67M6B3OCCL3/graph.json","events_json":"https://pith.science/api/pith-number/DOMQG7QUADMLWKJ67M6B3OCCL3/events.json","paper":"https://pith.science/paper/DOMQG7QU"},"agent_actions":{"view_html":"https://pith.science/pith/DOMQG7QUADMLWKJ67M6B3OCCL3","download_json":"https://pith.science/pith/DOMQG7QUADMLWKJ67M6B3OCCL3.json","view_paper":"https://pith.science/paper/DOMQG7QU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.01404&json=true","fetch_graph":"https://pith.science/api/pith-number/DOMQG7QUADMLWKJ67M6B3OCCL3/graph.json","fetch_events":"https://pith.science/api/pith-number/DOMQG7QUADMLWKJ67M6B3OCCL3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DOMQG7QUADMLWKJ67M6B3OCCL3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DOMQG7QUADMLWKJ67M6B3OCCL3/action/storage_attestation","attest_author":"https://pith.science/pith/DOMQG7QUADMLWKJ67M6B3OCCL3/action/author_attestation","sign_citation":"https://pith.science/pith/DOMQG7QUADMLWKJ67M6B3OCCL3/action/citation_signature","submit_replication":"https://pith.science/pith/DOMQG7QUADMLWKJ67M6B3OCCL3/action/replication_record"}},"created_at":"2026-05-18T00:24:26.475470+00:00","updated_at":"2026-05-18T00:24:26.475470+00:00"}