{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UPSJKTHWEPDTL6AY4XPCQZZWXH","short_pith_number":"pith:UPSJKTHW","schema_version":"1.0","canonical_sha256":"a3e4954cf623c735f818e5de286736b9ea5900b931f6a34332fd18fedeb1a431","source":{"kind":"arxiv","id":"1509.05838","version":3},"attestation_state":"computed","paper":{"title":"The Dirichlet elliptic problem involving regional fractional Laplacian","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen","submitted_at":"2015-09-19T01:17:42Z","abstract_excerpt":"In this paper, we consider the solutions for elliptic equations involving regional fractional Laplacian \\begin{equation}\\label{0}\n  \\arraycolsep=1pt \\begin{array}{lll}\n  \\displaystyle (-\\Delta)^\\alpha_\\Omega u=f \\qquad & {\\rm in}\\quad \\Omega,\\\\[2mm] \\phantom{ (-\\Delta)^\\alpha }\n  \\displaystyle u=g\\quad & {\\rm on}\\quad \\partial \\Omega, \\end{array} \\end{equation} where $\\Omega$ is a bounded open domain in $\\mathbb{R}^N$ ($N\\ge 2$) with $C^2$ boundary $\\partial\\Omega$,\n  $\\alpha\\in(\\frac12,1)$ and the operator $(-\\Delta)^\\alpha_\\Omega$ denotes the regional fractional Laplacian. We prove that when"},"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":"1509.05838","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AP","submitted_at":"2015-09-19T01:17:42Z","cross_cats_sorted":[],"title_canon_sha256":"7b05b88ecd5f469d320e758f75d10c64b3ddd4d07d7f0167ae72319c117043ff","abstract_canon_sha256":"47fabd19c8195e2db8e79775dc38e09bb1f36ab68f304db232ae045eb4168355"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:28.542990Z","signature_b64":"7dNNg48d2hzNMqONvruDbGMyGLfcuey/gbe5gro+suaA68NG24BRE9fsXMG8J94kxCfBStWn97/T4ngeAJ7OCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3e4954cf623c735f818e5de286736b9ea5900b931f6a34332fd18fedeb1a431","last_reissued_at":"2026-05-18T00:51:28.542426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:28.542426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Dirichlet elliptic problem involving regional fractional Laplacian","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen","submitted_at":"2015-09-19T01:17:42Z","abstract_excerpt":"In this paper, we consider the solutions for elliptic equations involving regional fractional Laplacian \\begin{equation}\\label{0}\n  \\arraycolsep=1pt \\begin{array}{lll}\n  \\displaystyle (-\\Delta)^\\alpha_\\Omega u=f \\qquad & {\\rm in}\\quad \\Omega,\\\\[2mm] \\phantom{ (-\\Delta)^\\alpha }\n  \\displaystyle u=g\\quad & {\\rm on}\\quad \\partial \\Omega, \\end{array} \\end{equation} where $\\Omega$ is a bounded open domain in $\\mathbb{R}^N$ ($N\\ge 2$) with $C^2$ boundary $\\partial\\Omega$,\n  $\\alpha\\in(\\frac12,1)$ and the operator $(-\\Delta)^\\alpha_\\Omega$ denotes the regional fractional Laplacian. 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