{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:V4NQQOHBYIV4BBAW4IGDCDPBGL","short_pith_number":"pith:V4NQQOHB","schema_version":"1.0","canonical_sha256":"af1b0838e1c22bc08416e20c310de132f0dfe30920f4c2e2462f1fcfb2993ce6","source":{"kind":"arxiv","id":"1704.07560","version":2},"attestation_state":"computed","paper":{"title":"Local elliptic regularity for the Dirichlet fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrique Zuazua, Mahamadi Warma, Umberto Biccari","submitted_at":"2017-04-25T06:55:46Z","abstract_excerpt":"We analyze the local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian $(-\\Delta)^s$ on an arbitrary bounded open set $\\Omega\\subset\\mathbb{R}^N$. For $1<p<2$, we obtain regularity in the Besov space $B^{2s}_{p,2,\\textrm{loc}}(\\Omega)$, while for $2\\leq p<\\infty$ we show that the solutions belong to $W^{2s,p}_{\\textrm{loc}}(\\Omega)$. The key tool consists in analyzing carefully the elliptic equation satisfied by the solution locally, after cut-off, to later employ sharp regularity results in the whole space. We do it by two different method"},"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":"1704.07560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-25T06:55:46Z","cross_cats_sorted":[],"title_canon_sha256":"b97971089d4b819e336323afe703a4c0236083f61d4d88e79849a7c577dfaa83","abstract_canon_sha256":"ee4485862eaa7a70b290175aed760f0475076b52c966c56a125811bad115d09c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:50.246234Z","signature_b64":"P76b4pvS4f8XYcMakvI7CUAkPQfgIOCsmWpaIF6IluLh/DwtzLvL3ti3xGRvk1RTDgJN2MSPgYXDDTN4NqfVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af1b0838e1c22bc08416e20c310de132f0dfe30920f4c2e2462f1fcfb2993ce6","last_reissued_at":"2026-05-18T00:43:50.245539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:50.245539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local elliptic regularity for the Dirichlet fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrique Zuazua, Mahamadi Warma, Umberto Biccari","submitted_at":"2017-04-25T06:55:46Z","abstract_excerpt":"We analyze the local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian $(-\\Delta)^s$ on an arbitrary bounded open set $\\Omega\\subset\\mathbb{R}^N$. For $1<p<2$, we obtain regularity in the Besov space $B^{2s}_{p,2,\\textrm{loc}}(\\Omega)$, while for $2\\leq p<\\infty$ we show that the solutions belong to $W^{2s,p}_{\\textrm{loc}}(\\Omega)$. The key tool consists in analyzing carefully the elliptic equation satisfied by the solution locally, after cut-off, to later employ sharp regularity results in the whole space. We do it by two different method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07560","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1704.07560","created_at":"2026-05-18T00:43:50.245676+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.07560v2","created_at":"2026-05-18T00:43:50.245676+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07560","created_at":"2026-05-18T00:43:50.245676+00:00"},{"alias_kind":"pith_short_12","alias_value":"V4NQQOHBYIV4","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"V4NQQOHBYIV4BBAW","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"V4NQQOHB","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL","json":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL.json","graph_json":"https://pith.science/api/pith-number/V4NQQOHBYIV4BBAW4IGDCDPBGL/graph.json","events_json":"https://pith.science/api/pith-number/V4NQQOHBYIV4BBAW4IGDCDPBGL/events.json","paper":"https://pith.science/paper/V4NQQOHB"},"agent_actions":{"view_html":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL","download_json":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL.json","view_paper":"https://pith.science/paper/V4NQQOHB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.07560&json=true","fetch_graph":"https://pith.science/api/pith-number/V4NQQOHBYIV4BBAW4IGDCDPBGL/graph.json","fetch_events":"https://pith.science/api/pith-number/V4NQQOHBYIV4BBAW4IGDCDPBGL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL/action/storage_attestation","attest_author":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL/action/author_attestation","sign_citation":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL/action/citation_signature","submit_replication":"https://pith.science/pith/V4NQQOHBYIV4BBAW4IGDCDPBGL/action/replication_record"}},"created_at":"2026-05-18T00:43:50.245676+00:00","updated_at":"2026-05-18T00:43:50.245676+00:00"}