{"paper":{"title":"Regularity for eigenfunctions of Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Bernd Ammann, Catarina Carvalho, Victor Nistor","submitted_at":"2010-10-08T15:01:34Z","abstract_excerpt":"We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\\\"odinger operator. More precisely, let K_{a}^{m}(\\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \\sum_{1 \\le j \\le N} \\frac{b_j}{|x_j|} + \\sum_{1 \\le i < j \\le N} \\frac{c_{ij}}{|x_i-x_j|}, x in \\mathbb{R}^{3N}, b_j, c_{ij} in \\mathbb{R}. If u in L^2(\\mathbb{R}^{3N}) satisfies (-\\Delta + V) u = \\lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \\in \\mathbb{Z}_+ and all a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1712","kind":"arxiv","version":3},"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"}