{"paper":{"title":"Mass and Asymptotics associated to Fractional Hardy-Schr\\\"odinger Operators in Critical Regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Robert, Mingefeng Zhao, Nassif Ghoussoub, Shaya Shakerian","submitted_at":"2017-04-27T17:02:34Z","abstract_excerpt":"We consider linear and non-linear boundary value problems associated to the fractional Hardy-Schr\\\"odinger operator $ L_{\\gamma,\\alpha}: = ({-}{ \\Delta})^{\\frac{\\alpha}{2}}- \\frac{\\gamma}{|x|^{\\alpha}}$ on domains of $\\mathbb{R}^n$ containing the singularity $0$, where $0<\\alpha<2$ and $ 0 \\le \\gamma < \\gamma_H(\\alpha)$, the latter being the best constant in the fractional Hardy inequality on $\\mathbb{R}^n$. We tackle the existence of least-energy solutions for the borderline boundary value problem $(L_{\\gamma,\\alpha}-\\lambda I)u= {\\frac{u^{2^\\star_\\alpha(s)-1}}{|x|^s}}$ on $\\Omega$, where $0\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08658","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"}