{"paper":{"title":"Inverse Boundary Value Problem by Partial data for the Neumann-to-Dirichlet-map in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G. Uhlmann, M. Yamamoto, O. Imanuvilov","submitted_at":"2012-10-03T22:46:44Z","abstract_excerpt":"For the two dimensional Schr\\\"odinger equation in a bounded domain, we prove uniqueness of determination of potentials in $W^1_p(\\Omega),\\,\\, p>2$ in the case where we apply all possible Neumann data supported on an arbitrarily non-empty open set $\\widetilde\\Gamma$ of the boundary and observe the corresponding Dirichlet data on $\\widetilde{\\Gamma}$. An immediate consequence is that one can uniquely determine a conductivity in $W^3_p(\\Omega)$ with $p>2$ by measuring the voltage on an open subset of the boundary corresponding to current supported in the same set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1255","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"}