{"paper":{"title":"Condensers with touching plates and constrained minimum Riesz and Green energy problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B. Fuglede, D.P. Hardin, E.B. Saff, N. Zorii, P.D. Dragnev","submitted_at":"2017-11-15T10:13:30Z","abstract_excerpt":"We study minimum energy problems relative to the $\\alpha$-Riesz kernel $|x-y|^{\\alpha-n}$, $\\alpha\\in(0,2]$, over signed Radon measures $\\mu$ on $\\mathbb R^n$, $n\\geqslant3$, associated with a generalized condenser $(A_1,A_2)$, where $A_1$ is a relatively closed subset of a domain $D$ and $A_2=\\mathbb R^n\\setminus D$. We show that, though $A_2\\cap\\mathrm{Cl}_{\\mathbb R^n}A_1$ may have nonzero capacity, this minimum energy problem is uniquely solvable (even in the presence of an external field) if we restrict ourselves to $\\mu$ with $\\mu^+\\leqslant\\xi$, where a constraint $\\xi$ is properly chos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05484","kind":"arxiv","version":2},"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"}