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In this paper, we prove that problem $$ \\begin{array}{lll}\n  (-\\Delta)^\\a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.02490","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2015-05-11T05:44:04Z","cross_cats_sorted":[],"title_canon_sha256":"ab6734ae42a7a98f794ecb13de4a0565b3536f934d10524081ae83ebd8c51ca4","abstract_canon_sha256":"0152743064cc11814b7c286e2a256b9e2a8f8668cee8192dc3bfc39f84bcd540"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:18.644280Z","signature_b64":"cpZBI9V4aq07Khtwuy5QXAHOsk5vH2puOVF5YmESM5wWEaWlGJB3brt5us1iWH7tNFktDgKc1BMtNSIeQzU8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91eb0908e6e87b2ee034a56f4a84644b014e671ec3618a079d9f4388ff32c1a2","last_reissued_at":"2026-05-18T02:16:18.643425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:18.643425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $x\\in\\partial\\Omega$. 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