{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:FLDQ36Z3DHEJGH4OOQZT7GSY6Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"22cb515d9116999bdc519731c0836b18cd64b60e48c18e60c17652d427eb6f3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-06-17T17:45:07Z","title_canon_sha256":"f81308d6a0cc03652eaba6ec1db0183400d189ce033bd78792232632ff10a4cb"},"schema_version":"1.0","source":{"id":"2006.10026","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.10026","created_at":"2026-07-05T01:19:40Z"},{"alias_kind":"arxiv_version","alias_value":"2006.10026v2","created_at":"2026-07-05T01:19:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.10026","created_at":"2026-07-05T01:19:40Z"},{"alias_kind":"pith_short_12","alias_value":"FLDQ36Z3DHEJ","created_at":"2026-07-05T01:19:40Z"},{"alias_kind":"pith_short_16","alias_value":"FLDQ36Z3DHEJGH4O","created_at":"2026-07-05T01:19:40Z"},{"alias_kind":"pith_short_8","alias_value":"FLDQ36Z3","created_at":"2026-07-05T01:19:40Z"}],"graph_snapshots":[{"event_id":"sha256:b9baa41de521558e4632048dc3a08e9647cffc985739516da39d29f22374eb1b","target":"graph","created_at":"2026-07-05T01:19:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.10026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if $u$ is a weak solution of $(-\\Delta)^s u=f$ in $\\Omega$, $\\mathcal N_s u=0$ in $\\Omega^c$, then $u$ is $C^\\alpha$ up tp the boundary for some $\\alpha>0$. Moreover, in case $s>\\frac12$, we then show that $u\\in C^{2s-1+\\alpha}(\\overline\\Omega)$. To prove these results we need, among other things, a delicate Moser iteration on the boundary with some logarithmic corrections. Our methods allow us to treat as well the Neumann problem for the regional fractional Laplacian, and","authors_text":"Alessandro Audrito, Juan-Carlos Felipe-Navarro, Xavier Ros-Oton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-06-17T17:45:07Z","title":"The Neumann problem for the fractional Laplacian: regularity up to the boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.10026","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:95e7fa3c7537ffd7a8f186ba66b342c400d761d9f17a1defc18ce0ba7854e108","target":"record","created_at":"2026-07-05T01:19:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"22cb515d9116999bdc519731c0836b18cd64b60e48c18e60c17652d427eb6f3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-06-17T17:45:07Z","title_canon_sha256":"f81308d6a0cc03652eaba6ec1db0183400d189ce033bd78792232632ff10a4cb"},"schema_version":"1.0","source":{"id":"2006.10026","kind":"arxiv","version":2}},"canonical_sha256":"2ac70dfb3b19c8931f8e74333f9a58f43c1ae267d32982e364c21046e15b1af1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ac70dfb3b19c8931f8e74333f9a58f43c1ae267d32982e364c21046e15b1af1","first_computed_at":"2026-07-05T01:19:40.447703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:19:40.447703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DjuSO+hjwbQE4OedGib6Jh/3k3YvA7f56zK/Q1yBBT3MGMmTjNP16Xu0zMbCCoXX4UMoIAy/ktqIl4+McsphBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:19:40.448123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.10026","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95e7fa3c7537ffd7a8f186ba66b342c400d761d9f17a1defc18ce0ba7854e108","sha256:b9baa41de521558e4632048dc3a08e9647cffc985739516da39d29f22374eb1b"],"state_sha256":"a395d397b9961aa57cb553d7be868addf6676b89a3c1a3e77a851616fbe6f893"}