{"paper":{"title":"Reconstruction of complex-valued tensors in the Maxwell system from knowledge of internal magnetic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chenxi Guo, Guillaume Bal","submitted_at":"2013-08-27T13:49:17Z","abstract_excerpt":"This paper concerns the reconstruction of a complex-valued anisotropic tensor $\\gamma=\\sigma+\\i\\omega\\varepsilon$ from knowledge of several internal magnetic fields $H$, where $H$ satisfies the anisotropic Maxwell system on a bounded domain with prescribed boundary conditions. We show that $\\gamma$ can be uniquely reconstructed with a loss of two derivatives from errors in the acquisition of $H$. A minimum number of 6 such functionals is sufficient to obtain a local reconstruction of $\\gamma$. In the special case where $\\gamma$ is close to a scalar tensor, boundary conditions are chosen by mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5872","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":""},"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"}