{"paper":{"title":"Boundary blow-up solutions to fractional elliptic equations in a measure framework","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hichem Hajaiej, Huyuan Chen, Ying Wang","submitted_at":"2015-05-11T05:44:04Z","abstract_excerpt":"Let $\\alpha\\in(0,1)$, $\\Omega$ be a bounded open domain in $R^N$ ($N\\ge 2$) with $C^2$ boundary $\\partial\\Omega$ and $\\omega$ be the Hausdorff measure on $\\partial\\Omega$.\n  We denote by $\\frac{\\partial^\\alpha \\omega}{\\partial \\vec{n}^\\alpha}$ a measure $$\\langle\\frac{\\partial^\\alpha \\omega}{\\partial \\vec{n}^\\alpha},f\\rangle=\\int_{\\partial\\Omega}\\frac{\\partial^\\alpha f(x)}{\\partial \\vec{n}_x^\\alpha} d\\omega(x),\\quad f\\in C^1(\\bar\\Omega),$$ where $\\vec{n}_x$ is the unit outward normal vector at point $x\\in\\partial\\Omega$. In this paper, we prove that problem $$ \\begin{array}{lll}\n  (-\\Delta)^\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02490","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"}