{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:RXVE36FAQFJEL5UDBIHP24NUAD","short_pith_number":"pith:RXVE36FA","schema_version":"1.0","canonical_sha256":"8dea4df8a0815245f6830a0efd71b400ed56d897e97528bb233e90cd486dfd89","source":{"kind":"arxiv","id":"1609.04256","version":1},"attestation_state":"computed","paper":{"title":"H\\\"older continuity of bounded, weak solutions of a variational system in the critical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nirav Shah","submitted_at":"2016-09-14T13:20:07Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^{2}$ be a bounded, Lipschitz domain. We consider bounded, weak solutions ($u\\in W^{1, 2}\\cap L^{\\infty}(\\Omega;\\mathbb{R}^N)$) of the vector-valued, Euler-Lagrange system: \\text{div } \\big( A(x, u)Du\\big)=g(x, u, Du)\\quad\\text{in }\\Omega.\n  Under natural growth conditions on the principal part and the inhomogeneity, but without any further restriction on the growth of the inhomogeneity (for example, via a smallness condition), we use a blow-up argument to prove that every bounded, weak solution of the system is H\\\"older continuous. Since the dimension of $\\Omega$ i"},"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":"1609.04256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-14T13:20:07Z","cross_cats_sorted":[],"title_canon_sha256":"891a35986d96c8aa39255384350de15df6fe35301a19096eb74617fa98af3a52","abstract_canon_sha256":"ee95982c3d5efd8377c535d3b41af6d8bc707fbd15908135acd59e8bfb41da2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:38.458248Z","signature_b64":"+SYfPSqoHk+Q+udTL9rBRHypkyOYXkOWhLAkFSHysE8E0FWjJxZakORl975kaX+2BNA1KfiZEXvl55/3Jo4bDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dea4df8a0815245f6830a0efd71b400ed56d897e97528bb233e90cd486dfd89","last_reissued_at":"2026-05-18T01:04:38.457542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:38.457542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"H\\\"older continuity of bounded, weak solutions of a variational system in the critical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nirav Shah","submitted_at":"2016-09-14T13:20:07Z","abstract_excerpt":"Let $\\Omega\\subset\\mathbb{R}^{2}$ be a bounded, Lipschitz domain. We consider bounded, weak solutions ($u\\in W^{1, 2}\\cap L^{\\infty}(\\Omega;\\mathbb{R}^N)$) of the vector-valued, Euler-Lagrange system: \\text{div } \\big( A(x, u)Du\\big)=g(x, u, Du)\\quad\\text{in }\\Omega.\n  Under natural growth conditions on the principal part and the inhomogeneity, but without any further restriction on the growth of the inhomogeneity (for example, via a smallness condition), we use a blow-up argument to prove that every bounded, weak solution of the system is H\\\"older continuous. Since the dimension of $\\Omega$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04256","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":"1609.04256","created_at":"2026-05-18T01:04:38.457651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04256v1","created_at":"2026-05-18T01:04:38.457651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04256","created_at":"2026-05-18T01:04:38.457651+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXVE36FAQFJE","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXVE36FAQFJEL5UD","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXVE36FA","created_at":"2026-05-18T12:30:41.710351+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/RXVE36FAQFJEL5UDBIHP24NUAD","json":"https://pith.science/pith/RXVE36FAQFJEL5UDBIHP24NUAD.json","graph_json":"https://pith.science/api/pith-number/RXVE36FAQFJEL5UDBIHP24NUAD/graph.json","events_json":"https://pith.science/api/pith-number/RXVE36FAQFJEL5UDBIHP24NUAD/events.json","paper":"https://pith.science/paper/RXVE36FA"},"agent_actions":{"view_html":"https://pith.science/pith/RXVE36FAQFJEL5UDBIHP24NUAD","download_json":"https://pith.science/pith/RXVE36FAQFJEL5UDBIHP24NUAD.json","view_paper":"https://pith.science/paper/RXVE36FA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04256&json=true","fetch_graph":"https://pith.science/api/pith-number/RXVE36FAQFJEL5UDBIHP24NUAD/graph.json","fetch_events":"https://pith.science/api/pith-number/RXVE36FAQFJEL5UDBIHP24NUAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXVE36FAQFJEL5UDBIHP24NUAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXVE36FAQFJEL5UDBIHP24NUAD/action/storage_attestation","attest_author":"https://pith.science/pith/RXVE36FAQFJEL5UDBIHP24NUAD/action/author_attestation","sign_citation":"https://pith.science/pith/RXVE36FAQFJEL5UDBIHP24NUAD/action/citation_signature","submit_replication":"https://pith.science/pith/RXVE36FAQFJEL5UDBIHP24NUAD/action/replication_record"}},"created_at":"2026-05-18T01:04:38.457651+00:00","updated_at":"2026-05-18T01:04:38.457651+00:00"}