{"paper":{"title":"Inverse anisotropic conductivity from power densities in dimension $n\\ge 3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Francois Monard, Guillaume Bal","submitted_at":"2012-08-29T21:31:06Z","abstract_excerpt":"We investigate the problem of reconstructing a fully anisotropic conductivity tensor $\\gamma$ from internal functionals of the form $\\nabla u\\cdot\\gamma\\nabla u$ where $u$ solves $\\nabla\\cdot(\\gamma\\nabla u) = 0$ over a given bounded domain $X$ with prescribed Dirichlet boundary condition. This work motivated by hybrid medical imaging methods covers the case $n\\ge 3$, following the previously published case $n=2$ \\cite{Monard2011}. Under knowledge of enough such functionals, and writing $\\gamma = \\tau \\tilde \\gamma$ ($\\det \\tilde\\gamma = 1$) with $\\tau$ a positive scalar function, we show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6029","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"}