{"paper":{"title":"Determining both leading coefficient and source in a nonlocal elliptic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yi-Hsuan Lin","submitted_at":"2023-12-25T04:24:35Z","abstract_excerpt":"In this short note, we investigate an inverse source problem associated with a nonlocal elliptic equation\n  $\\left( -\\nabla \\cdot \\sigma \\nabla \\right)^s u =F$ that is given in a bounded open set $\\Omega\\subset \\mathbb{R}^n$, for $n\\geq 3$ and $0<s<1$. We demonstrate both $\\sigma$ and $F$ can be determined uniquely by using the exterior Dirichlet-to-Neumann (DN) map in $\\Omega_e:=\\mathbb{R}^n\\setminus \\overline{\\Omega}$. The result is intriguing in that analogous theory cannot be true for the local case generally, that is, $s=1$. The key ingredients to prove the uniqueness is based on the uniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.15607","kind":"arxiv","version":1},"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/2312.15607/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"}