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We find the regularity of solutions and determine the exact Dirichlet domain $D_{a,s,q}$ (the space of solutions $u$ with $f\\in H_q^s(\\overline\\Omega )$) in cases where $\\Omega $ has limited smoothness $C^{1+\\tau }$, for $2"},"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":"2004.10134","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-04-21T16:26:34Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"19a53a7e2c05790c6f65d1d3544f130377231bdef1482602a1bb2538a499f932","abstract_canon_sha256":"ddbf366fa0d04ad56b2bdbff9a5771490fe327e8be544bdfbfd4e656078db7b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:00:53.834670Z","signature_b64":"Oi5qfNZsuQhRwRwGwCeXZAfWOYPLpws5ztT/3LyaE7tQa2GuKSDtso1Omyqeizb5XPiGHZHXHzldW/v6dNUBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98d6b80a5e6a38a5eb1a85079a6500315d3300fe306eb4f5ed90654186ac49ec","last_reissued_at":"2026-07-05T06:00:53.834303Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:00:53.834303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional-Order Operators on Nonsmooth Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Gerd Grubb, Helmut Abels","submitted_at":"2020-04-21T16:26:34Z","abstract_excerpt":"The fractional Laplacian $(-\\Delta )^a$, $a\\in(0,1)$, and its generalizations to variable-coefficient $2a$-order pseudodifferential operators $P$, are studied in $L_q$-Sobolev spaces of Bessel-potential type $H^s_q$. 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