{"paper":{"title":"Inner Riesz balayage in minimum energy problems with external fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Natalia Zorii","submitted_at":"2023-06-22T10:39:13Z","abstract_excerpt":"For the Riesz kernel $\\kappa_\\alpha(x,y):=|x-y|^{\\alpha-n}$ on $\\mathbb R^n$, where $n\\geqslant2$, $\\alpha\\in(0,2]$, and $\\alpha<n$, we consider the problem of minimizing the Gauss functional \\[\\int\\kappa_\\alpha(x,y)\\,d(\\mu\\otimes\\mu)(x,y)+2\\int f\\,d\\mu,\\quad\\text{where $f:=-\\int\\kappa_\\alpha(\\cdot,y)\\,d\\omega(y)$},\\] $\\omega$ being a given positive (Radon) measure on $\\mathbb R^n$, and $\\mu$ ranging over all positive measures of finite energy, concentrated on $A\\subset\\mathbb R^n$ and having unit total mass. We prove that if $A$ is a quasiclosed set of nonzero inner capacity $c_*(A)$, and if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.12788","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.12788/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}