{"paper":{"title":"Reconstruction of isotropic conductivities from non smooth electric fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.AP","authors_text":"Marc Briane (IRMAR)","submitted_at":"2018-02-12T12:57:53Z","abstract_excerpt":"In this paper we study the isotropic realizability of a given non smooth gradient field $\\nabla u$ defined in $\\mathbb{R}^d$, namely when one can reconstruct an isotropic conductivity $\\sigma>0$ such that $\\sigma\\nabla u$ is divergence free in $\\mathbb{R}^d$. On the one hand, in the case where $\\nabla u$ is non-vanishing, uniformly continuous in $\\mathbb{R}^d$ and $\\triangle u$ is a bounded function in $\\mathbb{R}^d$, we prove the isotropic realizability of $\\nabla u$ using the associated gradient flow combined with the DiPerna, Lions approach for solving ordinary differential equations in sui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04857","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"}