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When $\\Omega$ is an infinite strip, i.e., a domain bounded by two parallel straight lines, there exists a unique one-dimensional solution (called the trivial solution) to this probl"},"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":"2606.19885","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-18T07:44:21Z","cross_cats_sorted":[],"title_canon_sha256":"33e70317bce27b1977c0e8754929d7e83fe91ebe02863bd0222e4593b23610a2","abstract_canon_sha256":"9897eeaddf6273bb1663c53cc2040b90b4268071715ba442c16ea78d9c72c889"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:37.772515Z","signature_b64":"hOn/Gr+Y9t2z/pdQlusp/TjmFzI+bBjE2DCfBgY+609NWi6itZ4q5Ke8e5pNjhB8+oiUdtNDDN5C73r4U57xAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39192aa3652dd7ec96314e48f2606c69e75196cc13aa31bcdb4adba58aeb6da7","last_reissued_at":"2026-06-19T16:12:37.772155Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:37.772155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bifurcation of overdetermined capillary problems in a strip domain","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pieralberto Sicbaldi, Yuanyuan Lian","submitted_at":"2026-06-18T07:44:21Z","abstract_excerpt":"In this paper, we consider the classical overdetermined capillary problem:\n  \\begin{equation*}\n  \\begin{cases}\n  \\mathrm{div} \\left(\\frac{\\nabla u}{\\sqrt{1+|\\nabla u|^2}}\\right) - bu =0 &~~\\mbox{in}~~ \\Omega,\n  \\partial_{\\nu} u=\\kappa &~~\\mbox{on}~~\\partial\\Omega,\n  u=c &~~\\mbox{on}~~\\partial\\Omega,\n  \\end{cases} \\end{equation*}\n  where $b$, $c$ and $\\kappa$ are positive constants, and $\\Omega\\subset \\mathbb{R}^2$. 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