{"paper":{"title":"The Calder\\'on problem is an inverse source problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jan Cristina","submitted_at":"2015-11-05T11:33:48Z","abstract_excerpt":"We prove that uniqueness for the Calder\\'on problem on a Riemannian manifold with boundary follows from a hypothetical unique continuation property for the elliptic operator $\\Delta+V+(\\Lambda^{1}_{t}-q)\\otimes (\\Lambda^{2}_{t}-q)$ defined on $\\partial\\mathcal{M}^{2}\\times [0,1]$ where $V$ and $q$ are potentials and $\\Lambda^{i}_{t}$ is a Dirichlet-Neumann operator at depth $t$. This is done by showing that the difference of two Dirichlet-Neumann maps is equal to the Neumann boundary values of the solution to an inhomogeneous equation for said operator, where the source term is a measure suppo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01700","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":""},"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"}