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This answers negatively for large dimensions a question by Berestycki, Caffarelli and Nirenberg \\cite{bcn2}. In 1971, Serrin \\cite{serrin} proved that a bounded domain where such an overdetermined problem is solvable must"},"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":"1310.4528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-16T21:57:04Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"e8e2d7eeaf75088e03afae3c3b1797ecf85964a915dd6f29a29a25896404e596","abstract_canon_sha256":"62a9adfe6d75e0fca537f4efc7b11cd7456660d625fd0af81b6e9f4b70fd7788"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:06.128252Z","signature_b64":"Xh10sClTeA0q1TIZhgTO8kNE4I+68p+cmiJthzsz53fjlQubbiDi5y8tJrpGgO1WNyp2i2EAfplYbUVAHhaZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8c2bfa5d31d775b2b3a9728bb83db222187b97e4f2d93ca1525acbf946a02dc","last_reissued_at":"2026-05-18T01:28:06.127593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:06.127593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Serrin's Overdetermined Problem and Constant Mean Curvature Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Frank Pacard, Juncheng Wei, Manuel del Pino","submitted_at":"2013-10-16T21:57:04Z","abstract_excerpt":"For all $N \\geq 9$, we find smooth entire epigraphs in $\\R^N$, namely smooth domains of the form $\\Omega : = \\{x\\in \\R^N\\ / \\ x_N > F (x_1,\\ldots, x_{N-1})\\}$, which are not half-spaces and in which a problem of the form\n  $\\Delta u + f(u) = 0 $ in $\\Omega$ has a positive, bounded solution with 0 Dirichlet boundary data and constant Neumann boundary data on $\\partial \\Omega$. 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