{"paper":{"title":"Weighted minimum $\\alpha$-Green energy problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Natalia Zorii","submitted_at":"2025-05-04T21:31:53Z","abstract_excerpt":"For the $\\alpha$-Green kernel $g^\\alpha_D$ on a domain $D\\subset\\mathbb R^n$, $n\\geqslant2$, associated with the $\\alpha$-Riesz kernel $|x-y|^{\\alpha-n}$, where $\\alpha\\in(0,n)$ and $\\alpha\\leqslant2$, and a relatively closed set $F\\subset D$, we investigate the problem on minimizing the Gauss functional \\[\\int g^\\alpha_D(x,y)\\,d(\\mu\\otimes\\mu)(x,y)-2\\int g^\\alpha_D(x,y)\\,d(\\vartheta\\otimes\\mu)(x,y),\\] $\\vartheta$ being a given positive (Radon) measure concentrated on $D\\setminus F$, and $\\mu$ ranging over all probability measures of finite energy, supported in $D$ by $F$. For suitable $\\varth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02260","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.02260/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"}