{"paper":{"title":"Hardy-Sobolev equations with asymptotically vanishing singularity: Blow-up analysis for the minimal energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Saikat Mazumdar","submitted_at":"2017-02-12T02:48:56Z","abstract_excerpt":"We study the asymptotic behavior of a sequence of positive solutions $(u_{\\epsilon})_{\\epsilon >0}$ as $\\epsilon \\to 0$ to the family of equations \\begin{equation*} \\left\\{\\begin{array}{ll} \\Delta u_{\\epsilon}+a(x)u_{\\epsilon}= \\frac{u_{\\epsilon}^{2^*(s_{\\epsilon})-1}}{|x|^{s_{\\epsilon}}}& \\hbox{ in }\\Omega\\\\ u_{\\epsilon}=0 & \\hbox{ on }\\partial\\Omega. \\end{array}\\right. \\end{equation*} where $(s_{\\epsilon})_{\\epsilon >0}$ is a sequence of positive real numbers such that $\\lim \\limits_{\\epsilon \\rightarrow 0} s_{\\epsilon}=0$, $2^{*}(s_{\\epsilon}):= \\frac{2(n-s_{\\epsilon})}{n-2}$ and $\\Omega \\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03480","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"}