{"paper":{"title":"Lipschitz stability for the electrical impedance tomography problem: the complex case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elena Beretta, Elisa Francini","submitted_at":"2010-08-24T13:55:59Z","abstract_excerpt":"In this paper we investigate the boundary value problem ${div(\\gamma\\nabla u)=0 in \\Omega, u=f on \\partial\\Omega$ where $\\gamma$ is a complex valued $L^\\infty$ coefficient, satisfying a strong ellipticity condition. In Electrical Impedance Tomography, $\\gamma$ represents the admittance of a conducting body. An interesting issue is the one of determining $\\gamma$ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map $\\Lambda_\\gamma$. Under the above general assumptions this problem is an open issue.\n  In this paper we prove that, if we assume a priori that $\\gamma$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4046","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"}