{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:542ASJKGGPNNPCN5ZFGYASPZEF","short_pith_number":"pith:542ASJKG","schema_version":"1.0","canonical_sha256":"ef3409254633dad789bdc94d8049f9214b473db29ef07708ea593cad433a543c","source":{"kind":"arxiv","id":"2202.03017","version":1},"attestation_state":"computed","paper":{"title":"On a class of nonlocal problems with fractional gradient constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Azevedo, J.F. Rodrigues, L. Santos","submitted_at":"2022-02-07T09:14:11Z","abstract_excerpt":"We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type $|D^\\sigma u|\\leq g$, involving the distributional fractional Riesz gradient $D^\\sigma$, $0<\\sigma <1$, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems.\n  We also prove their convergence as $\\sigma\\nearrow1$ towards their local counterparts with the gradient constraint $|D u|\\leq g$."},"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":"2202.03017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-02-07T09:14:11Z","cross_cats_sorted":[],"title_canon_sha256":"c28fc547de53df048c2c6149aa2157c9d40592831809673e48c3751780c94686","abstract_canon_sha256":"468eccce3d247eae9d8caf29611250725cff7b686a06bf8c509efceca9760d0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:54:34.898970Z","signature_b64":"OSNg4jEJk97KdK6V6z1vS4Vmppv9HdTK5W8xJJtehmih7/bMkXTqlHK+wnP+HLIsoQmRZJnmVWfoVf+ZS+f8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef3409254633dad789bdc94d8049f9214b473db29ef07708ea593cad433a543c","last_reissued_at":"2026-07-05T03:54:34.898550Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:54:34.898550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a class of nonlocal problems with fractional gradient constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Azevedo, J.F. Rodrigues, L. Santos","submitted_at":"2022-02-07T09:14:11Z","abstract_excerpt":"We consider a Hilbertian and a charges approach to fractional gradient constraint problems of the type $|D^\\sigma u|\\leq g$, involving the distributional fractional Riesz gradient $D^\\sigma$, $0<\\sigma <1$, extending previous results on the existence of solutions and Lagrange multipliers of these nonlocal problems.\n  We also prove their convergence as $\\sigma\\nearrow1$ towards their local counterparts with the gradient constraint $|D u|\\leq g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.03017","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.03017/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2202.03017","created_at":"2026-07-05T03:54:34.898615+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.03017v1","created_at":"2026-07-05T03:54:34.898615+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.03017","created_at":"2026-07-05T03:54:34.898615+00:00"},{"alias_kind":"pith_short_12","alias_value":"542ASJKGGPNN","created_at":"2026-07-05T03:54:34.898615+00:00"},{"alias_kind":"pith_short_16","alias_value":"542ASJKGGPNNPCN5","created_at":"2026-07-05T03:54:34.898615+00:00"},{"alias_kind":"pith_short_8","alias_value":"542ASJKG","created_at":"2026-07-05T03:54:34.898615+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/542ASJKGGPNNPCN5ZFGYASPZEF","json":"https://pith.science/pith/542ASJKGGPNNPCN5ZFGYASPZEF.json","graph_json":"https://pith.science/api/pith-number/542ASJKGGPNNPCN5ZFGYASPZEF/graph.json","events_json":"https://pith.science/api/pith-number/542ASJKGGPNNPCN5ZFGYASPZEF/events.json","paper":"https://pith.science/paper/542ASJKG"},"agent_actions":{"view_html":"https://pith.science/pith/542ASJKGGPNNPCN5ZFGYASPZEF","download_json":"https://pith.science/pith/542ASJKGGPNNPCN5ZFGYASPZEF.json","view_paper":"https://pith.science/paper/542ASJKG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.03017&json=true","fetch_graph":"https://pith.science/api/pith-number/542ASJKGGPNNPCN5ZFGYASPZEF/graph.json","fetch_events":"https://pith.science/api/pith-number/542ASJKGGPNNPCN5ZFGYASPZEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/542ASJKGGPNNPCN5ZFGYASPZEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/542ASJKGGPNNPCN5ZFGYASPZEF/action/storage_attestation","attest_author":"https://pith.science/pith/542ASJKGGPNNPCN5ZFGYASPZEF/action/author_attestation","sign_citation":"https://pith.science/pith/542ASJKGGPNNPCN5ZFGYASPZEF/action/citation_signature","submit_replication":"https://pith.science/pith/542ASJKGGPNNPCN5ZFGYASPZEF/action/replication_record"}},"created_at":"2026-07-05T03:54:34.898615+00:00","updated_at":"2026-07-05T03:54:34.898615+00:00"}