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Krishnan","submitted_at":"2018-01-15T16:26:33Z","abstract_excerpt":"We study the inverse problem of determining the vector and scalar potentials $\\mathcal{A}(t,x)=\\left(A_{0},A_{1},\\cdots,A_{n}\\right)$ and $q(t,x)$, respectively, in the relativistic Schr\\\"odinger equation\n  \\begin{equation*}\n  \\Big{(}\\left(\\partial_{t}+A_{0}(t,x)\\right)^{2}-\\sum_{j=1}^{n}\\left(\\partial_{j}+A_{j}(t,x)\\right)^{2}+q(t,x)\\Big{)}u(t,x)=0\n  \\end{equation*}\n  in the region $Q=(0,T)\\times\\Omega$, where $\\Omega$ is a $C^{2}$ bounded domain in $\\mathbb{R}^{n}$ for $n\\geq 3$ and $T>\\mbox{diam}(\\Omega)$ from partial data on the boundary $\\partial Q$. We prove the unique determination of t"},"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":"1801.04866","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-15T16:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"f2eebc8f9b6e74ac3339967c6829a545f47a8536c55d5d97035cd6ce9967f141","abstract_canon_sha256":"2ce5d1ad272b2cf30ea4b112c444364a2f40e2b7d01e3b051417c7476f665a8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:49.079257Z","signature_b64":"B8ALVzrV2qjxcXexstxXYqG+yATDYrKSw5MpyuKLUjkL/J3wjYkyaFNJIO7854XpfQw4RM0n3xXfJvKltdcxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8eda0fbfd0b6ec4191b5f74fe5ac21b6208bcadd331e7016e8f21533896185da","last_reissued_at":"2026-05-17T23:42:49.078670Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:49.078670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An inverse problem for the relativistic Schr\\\"odinger equation with partial boundary data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Manmohan Vashisth, Venkateswaran P. Krishnan","submitted_at":"2018-01-15T16:26:33Z","abstract_excerpt":"We study the inverse problem of determining the vector and scalar potentials $\\mathcal{A}(t,x)=\\left(A_{0},A_{1},\\cdots,A_{n}\\right)$ and $q(t,x)$, respectively, in the relativistic Schr\\\"odinger equation\n  \\begin{equation*}\n  \\Big{(}\\left(\\partial_{t}+A_{0}(t,x)\\right)^{2}-\\sum_{j=1}^{n}\\left(\\partial_{j}+A_{j}(t,x)\\right)^{2}+q(t,x)\\Big{)}u(t,x)=0\n  \\end{equation*}\n  in the region $Q=(0,T)\\times\\Omega$, where $\\Omega$ is a $C^{2}$ bounded domain in $\\mathbb{R}^{n}$ for $n\\geq 3$ and $T>\\mbox{diam}(\\Omega)$ from partial data on the boundary $\\partial Q$. 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