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We show that if $n\\geq 3$ and $u\\in C^{2}(\\mathbb{B}^{n},\\mathbb{R}^n) \\cap C(\\overline{\\mathbb{B}^{n}},\\mathbb{R}^n )$ is a solution to the hyperbolic Poisson equation, then it has the representation $u=P_{h}[\\phi]-G_{ h}[\\psi"},"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":"1607.05374","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-19T02:18:04Z","cross_cats_sorted":[],"title_canon_sha256":"e19f97c76fe7cafa79d5893d3daa853c1b9f6da2a714479d2cab48c761deaf73","abstract_canon_sha256":"7756a9c8adaa43e2a08d163574542f9a1fc6bd1c712a8f5270fda860add32f80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:05:35.527300Z","signature_b64":"PaCEkYJaUpHYvPAnN2mneG5ZSl4O5x3nJPTzP7WVQBvT5LDFDLK6lghIv9BS1FrS+UO9UTLMm4qlsysaph8nCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56accd2bc5b61072c05469f9d6e604a3c2221341133444271fd7cb84dff58d92","last_reissued_at":"2026-07-05T02:05:35.526827Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:05:35.526827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Lipschitz continuity of solutions of hyperbolic Poisson's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antti Rasila, Jiaolong Chen, Manzi Huang, Xiantao Wang","submitted_at":"2016-07-19T02:18:04Z","abstract_excerpt":"In this paper, we investigate solutions of the hyperbolic Poisson equation $\\Delta_{h}u(x)=\\psi(x)$, where $\\psi\\in L^{\\infty}(\\mathbb{B}^{n}, \\mathbb{R}^n)$ and \\[ \\Delta_{h}u(x)= (1-|x|^2)^2\\Delta u(x)+2(n-2)(1-|x|^2)\\sum_{i=1}^{n} x_{i} \\frac{\\partial u}{\\partial x_{i}}(x) \\] is the hyperbolic Laplace operator in the $n$-dimensional space $\\mathbb{R}^n$ for $n\\ge 2$. 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