{"paper":{"title":"Inverse problems for fractional equations with a minimal number of measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Yi-Hsuan Lin","submitted_at":"2022-03-06T17:08:05Z","abstract_excerpt":"In this paper, we study several inverse problems associated with a fractional differential equation of the following form:\n  \\[\n  (-\\Delta)^s u(x)+\\sum_{k=0}^N a^{(k)}(x) [u(x)]^k=0,\\ \\ 0<s<1,\\ N\\in\\mathbb{N}\\cup\\{0\\}\\cup\\{\\infty\\},\n  \\] which is given in a bounded domain $\\Omega\\subset\\mathbb{R}^n$, $n\\geq 1$. For any finite $N$, we show that $a^{(k)}(x)$, $k=0,1,\\ldots, N$, can be uniquely determined by $N+1$ different pairs of Cauchy data in $\\Omega_e:=\\mathbb{R}^n\\backslash\\overline{\\Omega}$. If $N=\\infty$, the uniqueness result is established by using infinitely many pairs of Cauchy data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.03010","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.03010/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}