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We show that $\\Omega $ is a ball and $u$ satisfies "},"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":"1512.05126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-16T10:50:45Z","cross_cats_sorted":[],"title_canon_sha256":"81ca9371be458b278d374ee9b6e0cb8365b8b21a91323e71a3683b4d1eb52a68","abstract_canon_sha256":"725ebbfd7ee8c2f91a4bfaf8b6a770b3ff6a5eaefe7c37b0c311e2fbb84129de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:13.426291Z","signature_b64":"90yp4yPWS2AyMui7apfU6Ep3UMew2eH8VI+xGBdwTWdMAEo1pTMZvdqaAv5aOHDN8NJX/4grPIK5LJPGUOhOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b945908a0fdf6b18d10b607b571db05d78efdeb41b8387f01e9ae33818bb9d7","last_reissued_at":"2026-05-18T01:24:13.425758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:13.425758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetry for a general class of overdetermined elliptic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Friedemann Brock","submitted_at":"2015-12-16T10:50:45Z","abstract_excerpt":"Let $\\Omega $ be a bounded domain in $\\mathbb{R} ^N $, and let $u\\in C^1 (\\overline{\\Omega }) $ be a weak solution of the following overdetermined BVP: $-\\nabla (g(|\\nabla u|)|\\nabla u|^{-1} \\nabla u )=f(|x|,u)$, $ u>0 $ in $\\Omega $ and $u(x)=0, \\ |\\nabla u (x)| =\\lambda (|x|)$ on $\\partial \\Omega $, where $g\\in C([0,+\\infty ))\\cap C^1 ((0,+\\infty ) ) $ with $g(0)=0$, $g'(t)>0$ for $t>0$, $f\\in C([0,+\\infty )) \\times [0, +\\infty ) )$, $f$ is nonincreasing in $|x|$, $\\lambda \\in C([0, +\\infty )) $ and $\\lambda $ is positive and nondecreasing. 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