{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4T57IBME4L45DQEWFBLE3V6M3W","short_pith_number":"pith:4T57IBME","schema_version":"1.0","canonical_sha256":"e4fbf40584e2f9d1c09628564dd7ccddb001572cc73a89a9cf842f484781cdac","source":{"kind":"arxiv","id":"1807.09497","version":1},"attestation_state":"computed","paper":{"title":"Fine boundary regularity for the degenerate fractional $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Iannizzotto, Marco Squassina, Sunra Mosconi","submitted_at":"2018-07-25T09:26:14Z","abstract_excerpt":"We consider a pseudo-differential equation driven by the fractional $p$-Laplacian with $p\\ge 2$ (degenerate case), with a bounded reaction $f$ and Dirichlet type conditions in a smooth domain $\\Omega$. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution $u$ of such equation exhibits a weighted H\\\"older regularity up to the boundary, that is, $u/d^s\\in C^\\alpha(\\overline\\Omega)$ for some $\\alpha\\in(0,1)$, $d$ being the distance from the boundary."},"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":"1807.09497","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-25T09:26:14Z","cross_cats_sorted":[],"title_canon_sha256":"ac2ba3ca2ffca305bdce1a9ee0de558da0d38e3d946464240be18ca0ac378a0d","abstract_canon_sha256":"2ed1d05df8431f0ad3ca7debb8d06627d8dbe764676851f590f8a8af58f29f35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:51.152450Z","signature_b64":"gj5onpJmLETg05YG58LFzolIMEydYG0gI+gH9ZrJNrGYUcuFfZiOWVl3k2yhS8cBv7Tgu8TNZiuoUkrzKX5bDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4fbf40584e2f9d1c09628564dd7ccddb001572cc73a89a9cf842f484781cdac","last_reissued_at":"2026-05-18T00:09:51.151763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:51.151763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fine boundary regularity for the degenerate fractional $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Iannizzotto, Marco Squassina, Sunra Mosconi","submitted_at":"2018-07-25T09:26:14Z","abstract_excerpt":"We consider a pseudo-differential equation driven by the fractional $p$-Laplacian with $p\\ge 2$ (degenerate case), with a bounded reaction $f$ and Dirichlet type conditions in a smooth domain $\\Omega$. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution $u$ of such equation exhibits a weighted H\\\"older regularity up to the boundary, that is, $u/d^s\\in C^\\alpha(\\overline\\Omega)$ for some $\\alpha\\in(0,1)$, $d$ being the distance from the boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09497","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":"1807.09497","created_at":"2026-05-18T00:09:51.151856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.09497v1","created_at":"2026-05-18T00:09:51.151856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09497","created_at":"2026-05-18T00:09:51.151856+00:00"},{"alias_kind":"pith_short_12","alias_value":"4T57IBME4L45","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4T57IBME4L45DQEW","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4T57IBME","created_at":"2026-05-18T12:32:05.422762+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.00910","citing_title":"Continuity of solutions to a nonlinear fractional diffusion equation","ref_index":16,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W","json":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W.json","graph_json":"https://pith.science/api/pith-number/4T57IBME4L45DQEWFBLE3V6M3W/graph.json","events_json":"https://pith.science/api/pith-number/4T57IBME4L45DQEWFBLE3V6M3W/events.json","paper":"https://pith.science/paper/4T57IBME"},"agent_actions":{"view_html":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W","download_json":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W.json","view_paper":"https://pith.science/paper/4T57IBME","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.09497&json=true","fetch_graph":"https://pith.science/api/pith-number/4T57IBME4L45DQEWFBLE3V6M3W/graph.json","fetch_events":"https://pith.science/api/pith-number/4T57IBME4L45DQEWFBLE3V6M3W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W/action/storage_attestation","attest_author":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W/action/author_attestation","sign_citation":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W/action/citation_signature","submit_replication":"https://pith.science/pith/4T57IBME4L45DQEWFBLE3V6M3W/action/replication_record"}},"created_at":"2026-05-18T00:09:51.151856+00:00","updated_at":"2026-05-18T00:09:51.151856+00:00"}