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Serrin's celebrated symmetry theorem states that, if the normal derivative $u_\\nu$ is constant on $\\Gamma$, then $\\Omega$ must be a ball.\n  In [CMS2], it has been conjectured that Serrin's theorem may be obtained by stability in the following way: first, for a solution $u$ prove the estimate"},"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":"1501.07531","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-29T18:17:58Z","cross_cats_sorted":[],"title_canon_sha256":"feb4bc654da022af7015363e560b7b9b4970123163e0a51c5c2305e93db78e3a","abstract_canon_sha256":"c478185643a75c920813d38cbe9afa37027379bc449ddd9acbdaef157deb6415"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:45.111130Z","signature_b64":"Ih7B4jEf6Lu5jkK4DD4XJeShba6DYvBQnEsP5ew15t+OdhgF2hYtSJ3DlrzZKMQxs5GtYpfcb3d47QhRM7cFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3a4b81dd135cbd2a87a88dc3e0f297b6357240b7fc3db60b98d876ed53aa889","last_reissued_at":"2026-05-18T02:03:45.110626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:45.110626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetry and linear stability in Serrin's overdetermined problem via the stability of the parallel surface problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giulio Ciraolo, Rolando Magnanini, Vincenzo Vespri","submitted_at":"2015-01-29T18:17:58Z","abstract_excerpt":"We consider the solution of the problem $$ -\\Delta u=f(u) \\ \\mbox{ and } \\ u>0 \\ \\ \\mbox{ in } \\ \\Omega, \\ \\ u=0 \\ \\mbox{ on } \\ \\Gamma, $$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^N$ with boundary $\\Gamma$ of class $C^{2,\\tau}$, $0<\\tau<1$, and $f$ is a locally Lipschitz continuous non-linearity. Serrin's celebrated symmetry theorem states that, if the normal derivative $u_\\nu$ is constant on $\\Gamma$, then $\\Omega$ must be a ball.\n  In [CMS2], it has been conjectured that Serrin's theorem may be obtained by stability in the following way: first, for a solution $u$ prove the estimate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07531","kind":"arxiv","version":3},"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":"1501.07531","created_at":"2026-05-18T02:03:45.110701+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.07531v3","created_at":"2026-05-18T02:03:45.110701+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07531","created_at":"2026-05-18T02:03:45.110701+00:00"},{"alias_kind":"pith_short_12","alias_value":"UOSLQHORGXF5","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UOSLQHORGXF5FKD2","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UOSLQHOR","created_at":"2026-05-18T12:29:44.643036+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/UOSLQHORGXF5FKD2RDOD4DZJPN","json":"https://pith.science/pith/UOSLQHORGXF5FKD2RDOD4DZJPN.json","graph_json":"https://pith.science/api/pith-number/UOSLQHORGXF5FKD2RDOD4DZJPN/graph.json","events_json":"https://pith.science/api/pith-number/UOSLQHORGXF5FKD2RDOD4DZJPN/events.json","paper":"https://pith.science/paper/UOSLQHOR"},"agent_actions":{"view_html":"https://pith.science/pith/UOSLQHORGXF5FKD2RDOD4DZJPN","download_json":"https://pith.science/pith/UOSLQHORGXF5FKD2RDOD4DZJPN.json","view_paper":"https://pith.science/paper/UOSLQHOR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.07531&json=true","fetch_graph":"https://pith.science/api/pith-number/UOSLQHORGXF5FKD2RDOD4DZJPN/graph.json","fetch_events":"https://pith.science/api/pith-number/UOSLQHORGXF5FKD2RDOD4DZJPN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UOSLQHORGXF5FKD2RDOD4DZJPN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UOSLQHORGXF5FKD2RDOD4DZJPN/action/storage_attestation","attest_author":"https://pith.science/pith/UOSLQHORGXF5FKD2RDOD4DZJPN/action/author_attestation","sign_citation":"https://pith.science/pith/UOSLQHORGXF5FKD2RDOD4DZJPN/action/citation_signature","submit_replication":"https://pith.science/pith/UOSLQHORGXF5FKD2RDOD4DZJPN/action/replication_record"}},"created_at":"2026-05-18T02:03:45.110701+00:00","updated_at":"2026-05-18T02:03:45.110701+00:00"}