{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:I677AS7KCQYMNN25LPDNMW2MMI","short_pith_number":"pith:I677AS7K","schema_version":"1.0","canonical_sha256":"47bff04bea1430c6b75d5bc6d65b4c6222e18e4367af88347edae6f256f7cdc7","source":{"kind":"arxiv","id":"1903.12496","version":1},"attestation_state":"computed","paper":{"title":"Global Schauder estimates for the $p$-Laplace system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Cianchi, Dominic Breit, Lars Diening, Sebastian Schwarzacher","submitted_at":"2019-03-29T13:01:10Z","abstract_excerpt":"An optimal first-order global regularity theory, in spaces of functions defined in terms of oscillations, is established for solutions to Dirichlet problems for the $p$-Laplace equation and system, with right-hand side in divergence form. The exact mutual dependence among the regularity of the solution, of the datum on the right-hand side, and of the boundary of the domain in these spaces is exhibited. A comprehensive formulation of our results is given in terms of Campanato seminorms. New regularity results in customary function spaces, such as H\\\"older, $\\mathrm{BMO}$ and $\\mathrm{VMO}$ spac"},"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":"1903.12496","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-29T13:01:10Z","cross_cats_sorted":[],"title_canon_sha256":"dda28a106d5121e3310b3b6c016667a5c82eada7276c1e2908c43829ce0f56a7","abstract_canon_sha256":"50c250e4e6eb63cf2e401c6930d876d3db8459432273c54cbacc8e0c72a37c3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:53.883290Z","signature_b64":"G2oFvK2N3oYHtosmjsSBTaIz+fKgTPxUAl4KXw4ssFJW5yc/2200tDoJBMMUfQW1Uw6REx+XpvBdQlwxoXbFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47bff04bea1430c6b75d5bc6d65b4c6222e18e4367af88347edae6f256f7cdc7","last_reissued_at":"2026-05-17T23:49:53.882852Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:53.882852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Schauder estimates for the $p$-Laplace system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Cianchi, Dominic Breit, Lars Diening, Sebastian Schwarzacher","submitted_at":"2019-03-29T13:01:10Z","abstract_excerpt":"An optimal first-order global regularity theory, in spaces of functions defined in terms of oscillations, is established for solutions to Dirichlet problems for the $p$-Laplace equation and system, with right-hand side in divergence form. The exact mutual dependence among the regularity of the solution, of the datum on the right-hand side, and of the boundary of the domain in these spaces is exhibited. A comprehensive formulation of our results is given in terms of Campanato seminorms. New regularity results in customary function spaces, such as H\\\"older, $\\mathrm{BMO}$ and $\\mathrm{VMO}$ spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12496","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":"1903.12496","created_at":"2026-05-17T23:49:53.882933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.12496v1","created_at":"2026-05-17T23:49:53.882933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12496","created_at":"2026-05-17T23:49:53.882933+00:00"},{"alias_kind":"pith_short_12","alias_value":"I677AS7KCQYM","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"I677AS7KCQYMNN25","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"I677AS7K","created_at":"2026-05-18T12:33:18.533446+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/I677AS7KCQYMNN25LPDNMW2MMI","json":"https://pith.science/pith/I677AS7KCQYMNN25LPDNMW2MMI.json","graph_json":"https://pith.science/api/pith-number/I677AS7KCQYMNN25LPDNMW2MMI/graph.json","events_json":"https://pith.science/api/pith-number/I677AS7KCQYMNN25LPDNMW2MMI/events.json","paper":"https://pith.science/paper/I677AS7K"},"agent_actions":{"view_html":"https://pith.science/pith/I677AS7KCQYMNN25LPDNMW2MMI","download_json":"https://pith.science/pith/I677AS7KCQYMNN25LPDNMW2MMI.json","view_paper":"https://pith.science/paper/I677AS7K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.12496&json=true","fetch_graph":"https://pith.science/api/pith-number/I677AS7KCQYMNN25LPDNMW2MMI/graph.json","fetch_events":"https://pith.science/api/pith-number/I677AS7KCQYMNN25LPDNMW2MMI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I677AS7KCQYMNN25LPDNMW2MMI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I677AS7KCQYMNN25LPDNMW2MMI/action/storage_attestation","attest_author":"https://pith.science/pith/I677AS7KCQYMNN25LPDNMW2MMI/action/author_attestation","sign_citation":"https://pith.science/pith/I677AS7KCQYMNN25LPDNMW2MMI/action/citation_signature","submit_replication":"https://pith.science/pith/I677AS7KCQYMNN25LPDNMW2MMI/action/replication_record"}},"created_at":"2026-05-17T23:49:53.882933+00:00","updated_at":"2026-05-17T23:49:53.882933+00:00"}