{"paper":{"title":"Isotropic realizability of electric fields around critical points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Marc Briane (IRMAR)","submitted_at":"2013-06-02T18:25:26Z","abstract_excerpt":"In this paper we study the isotropic realizability of a given regular gradient field $\\nabla u$ as an electric field, namely when $\\nabla u$ is solution of the equation $\\div\\left(\\si\\nabla u\\right)=0$ for some isotropic conductivity $\\si>0$. The case of a function $u$ without critical point was investigated in \\cite{BMT} thanks to a gradient flow approach. The presence of a critical point needs a specific treatment according to the behavior of the dynamical system around the point. The case of a saddle point is the most favorable and leads us to a characterization of the local isotropic reali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0236","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"}