{"paper":{"title":"Imaging of anisotropic conductivities from current densities in two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chenxi Guo, Fran\\c{c}ois Monard, Guillaume Bal","submitted_at":"2014-03-19T20:23:41Z","abstract_excerpt":"We consider the imaging of anisotropic conductivity tensors $\\gamma=(\\gamma_{ij})_{1\\leq i,j\\leq 2}$ from knowledge of several internal current densities $\\mathcal{J}=\\gamma\\nabla u$ where $u$ satisfies a second order elliptic equation $\\nabla\\cdot(\\gamma\\nabla u)=0$ on a bounded domain $X\\subset\\mathbb{R}^2$ with prescribed boundary conditions on $\\partial X$. We show that $\\gamma$ can be uniquely reconstructed from four {\\em well-chosen} functionals $\\mathcal{J}$ and that noise in the data is differentiated once during the reconstruction. The inversion procedure is local in the sense that (m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4964","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"}