{"paper":{"title":"A minimization problem involving a fractional Hardy-Sobolev type inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonella Ritorto","submitted_at":"2019-08-14T12:24:24Z","abstract_excerpt":"In this work, we obtain an existence of nontrivial solutions to a minimization problem involving a fractional Hardy-Sobolev type inequality in the case of inner singularity. Precisely, for $\\lambda>0$ we analyze the attainability of the optimal constant $$ \\mu_{\\alpha, \\lambda}(\\Omega):=\\inf\\left\\{ [u]^2_{s,\\Omega}+\\lambda\\int_{\\Omega}|u|^2 \\, dx \\colon u\\in H^s(\\Omega), \\, \\int_{\\Omega} \\frac{|u(x)|^{2_{s,\\alpha}}}{|x|^{\\alpha}} \\, dx=1 \\right\\}, $$ where $0<s<1, n>4s, 0<\\alpha<2s$, $2_{s,\\alpha}=\\frac{2(n-\\alpha)}{n-2s}$, and $\\Omega \\subset \\mathbb{R}^n$ be a bounded domain such that $0\\in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05095","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/1908.05095/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"}