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We obtain that any clas"},"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":"1509.05836","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2015-09-19T01:05:34Z","cross_cats_sorted":[],"title_canon_sha256":"14095f2eeb28f39f090375b4b07a1808a0f503e4378eb3306d69b80b8cf03d34","abstract_canon_sha256":"b3e3178fe7e195fdf9b2d6e62809236877863f2835358626876133d055ff0d1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:13.313866Z","signature_b64":"/hPFTWDsuKfDYAQ7h4LcVQEVfj69ZZqnVfwsRMcGDBzKjS+RtM5uAjwsvcpHbLE+CbFhoMiUMYiaj3pqkJpjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb81675f310212bb57b17990a031be6fd94dd45d4ddfd80642732442cbb1c6d5","last_reissued_at":"2026-05-18T01:31:13.313210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:13.313210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Huyuan Chen","submitted_at":"2015-09-19T01:05:34Z","abstract_excerpt":"In this paper, we classify the singularities of nonnegative solutions to fractional elliptic equation \\begin{equation}\\label{eq 0.1}\n  \\arraycolsep=1pt \\begin{array}{lll}\n  \\displaystyle (-\\Delta)^\\alpha u=u^p\\quad\n  &{\\rm in}\\quad \\Omega\\setminus\\{0\\},\\\\[2mm]\n  \\phantom{ (-\\Delta)^\\alpha }\n  \\displaystyle u=0\\quad\n  &{\\rm in}\\quad \\mathbb{R}^N\\setminus\\Omega, \\end{array} \\end{equation} where $p>1$, $\\Omega$ is a bounded, $C^2$ domain in $\\mathbb{R}^N$ containing the origin, $N\\ge2$ and the fractional Laplacian $(-\\Delta)^\\alpha$ is defined in the principle value sense. 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