{"paper":{"title":"Inverse Potential Problems for Divergence of Measures with Total Variation Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Cristobal Villalobos Guillen, Douglas P. Hardin, Edward B. Saff, Laurent Baratchart, Michael C. Northington","submitted_at":"2018-09-21T22:33:37Z","abstract_excerpt":"We study inverse problems for the Poisson equation with source term the divergence of an $\\mathbf{R}^3$-valued measure, that is, the potential $\\Phi$ satisfies $$\n  \\Delta \\Phi= \\text{div} \\boldsymbol{\\mu},\n  $$ and $\\boldsymbol{\\mu}$ is to be reconstructed knowing (a component of) the field grad $\\Phi$ on a set disjoint from the support of $\\boldsymbol{\\mu}$. Such problems arise in several electro-magnetic contexts in the quasi-static regime, for instance when recovering a remanent magnetization from measurements of its magnetic field. We develop methods for recovering $\\boldsymbol{\\mu}$ base"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08334","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"}