{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZCWWN77ZBVBYIBP4FSYOSXITES","short_pith_number":"pith:ZCWWN77Z","schema_version":"1.0","canonical_sha256":"c8ad66fff90d438405fc2cb0e95d1324957f075649dfad77dceb19542814a36e","source":{"kind":"arxiv","id":"1810.07645","version":1},"attestation_state":"computed","paper":{"title":"On the convergence in $H^1$-norm for the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Juan Pablo Borthagaray, Patrick Ciarlet Jr","submitted_at":"2018-10-17T16:23:14Z","abstract_excerpt":"We consider the numerical solution of the fractional Laplacian of index $s\\in(1/2,1)$ in a bounded domain $\\Omega$ with homogeneous boundary conditions. Its solution a priori belongs to the fractional order Sobolev space ${\\widetilde H}^s(\\Omega)$. For the Dirichlet problem and under suitable assumptions on the data, it can be shown that its solution is also in $H^1(\\Omega)$. In this case, if one uses the standard Lagrange finite element to discretize the problem, then both the exact and the computed solution belong to $H^1(\\Omega)$. A natural question is then whether one can obtain error esti"},"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":"1810.07645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-17T16:23:14Z","cross_cats_sorted":[],"title_canon_sha256":"8af0ec03249153f3305b855273b184be12d977475bdedfd5bbe4d033678f1fb7","abstract_canon_sha256":"9e31cdfb98246a40025f56f19ccd9e6942e027df2eacc813938eeab976ddf4fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:55.536092Z","signature_b64":"fKLFbr1X/9GcEv6z3IdQb+HELi3ymVcZwFppIwM0mKKBCwiq1Ea23Qign08ZWB0EIDH9lJ189Zm2+JO3Vmh/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8ad66fff90d438405fc2cb0e95d1324957f075649dfad77dceb19542814a36e","last_reissued_at":"2026-05-18T00:02:55.535360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:55.535360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the convergence in $H^1$-norm for the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Juan Pablo Borthagaray, Patrick Ciarlet Jr","submitted_at":"2018-10-17T16:23:14Z","abstract_excerpt":"We consider the numerical solution of the fractional Laplacian of index $s\\in(1/2,1)$ in a bounded domain $\\Omega$ with homogeneous boundary conditions. Its solution a priori belongs to the fractional order Sobolev space ${\\widetilde H}^s(\\Omega)$. For the Dirichlet problem and under suitable assumptions on the data, it can be shown that its solution is also in $H^1(\\Omega)$. In this case, if one uses the standard Lagrange finite element to discretize the problem, then both the exact and the computed solution belong to $H^1(\\Omega)$. A natural question is then whether one can obtain error esti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07645","kind":"arxiv","version":1},"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":"1810.07645","created_at":"2026-05-18T00:02:55.535475+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.07645v1","created_at":"2026-05-18T00:02:55.535475+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07645","created_at":"2026-05-18T00:02:55.535475+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZCWWN77ZBVBY","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZCWWN77ZBVBYIBP4","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZCWWN77Z","created_at":"2026-05-18T12:33:04.347982+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/ZCWWN77ZBVBYIBP4FSYOSXITES","json":"https://pith.science/pith/ZCWWN77ZBVBYIBP4FSYOSXITES.json","graph_json":"https://pith.science/api/pith-number/ZCWWN77ZBVBYIBP4FSYOSXITES/graph.json","events_json":"https://pith.science/api/pith-number/ZCWWN77ZBVBYIBP4FSYOSXITES/events.json","paper":"https://pith.science/paper/ZCWWN77Z"},"agent_actions":{"view_html":"https://pith.science/pith/ZCWWN77ZBVBYIBP4FSYOSXITES","download_json":"https://pith.science/pith/ZCWWN77ZBVBYIBP4FSYOSXITES.json","view_paper":"https://pith.science/paper/ZCWWN77Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.07645&json=true","fetch_graph":"https://pith.science/api/pith-number/ZCWWN77ZBVBYIBP4FSYOSXITES/graph.json","fetch_events":"https://pith.science/api/pith-number/ZCWWN77ZBVBYIBP4FSYOSXITES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZCWWN77ZBVBYIBP4FSYOSXITES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZCWWN77ZBVBYIBP4FSYOSXITES/action/storage_attestation","attest_author":"https://pith.science/pith/ZCWWN77ZBVBYIBP4FSYOSXITES/action/author_attestation","sign_citation":"https://pith.science/pith/ZCWWN77ZBVBYIBP4FSYOSXITES/action/citation_signature","submit_replication":"https://pith.science/pith/ZCWWN77ZBVBYIBP4FSYOSXITES/action/replication_record"}},"created_at":"2026-05-18T00:02:55.535475+00:00","updated_at":"2026-05-18T00:02:55.535475+00:00"}