{"paper":{"title":"Constrained minimum Riesz and Green energy problems for vector measures associated with a generalized condenser","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bent Fuglede, Natalia Zorii","submitted_at":"2018-02-19T18:24:12Z","abstract_excerpt":"For a finite collection $\\mathbf A=(A_i)_{i\\in I}$ of locally closed sets in $\\mathbb R^n$, $n\\geqslant3$, with the sign $\\pm1$ prescribed such that the oppositely charged plates are mutually disjoint, we consider the minimum energy problem relative to the $\\alpha$-Riesz kernel $|x-y|^{\\alpha-n}$, $\\alpha\\in(0,2]$, over positive vector Radon measures $\\boldsymbol\\mu=(\\mu^i)_{i\\in I}$ such that each $\\mu^i$, $i\\in I$, is carried by $A_i$ and normalized by $\\mu^i(A_i)=a_i\\in(0,\\infty)$. We show that, though the closures of oppositely charged plates may intersect each other even in a set of nonze"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07171","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"}