{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P4JJCMKEDZWYNU6YL5JC7W3RZE","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":"627b1ffdefe82b9b707a942737e8f02419fd1fa7557317d1382bea4b99804db6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-02T08:33:35Z","title_canon_sha256":"0eca1c9e5c1af13f841670381cb5907af1740ce4b133179b74d2384788f17cab"},"schema_version":"1.0","source":{"id":"1603.00612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00612","created_at":"2026-05-18T01:19:43Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00612v1","created_at":"2026-05-18T01:19:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00612","created_at":"2026-05-18T01:19:43Z"},{"alias_kind":"pith_short_12","alias_value":"P4JJCMKEDZWY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P4JJCMKEDZWYNU6Y","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P4JJCMKE","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:0f3b2e0a4ce81f46a317d11a8814613488199b027caaed8de3137077db88f70a","target":"graph","created_at":"2026-05-18T01:19:43Z","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"},"paper":{"abstract_excerpt":"In this article, by applying the well known method for dealing with $p$-Laplace type elliptic boundary value problems, the authors establish a sharp estimate for the decreasing rearrangement of the gradient of solutions to the Dirichlet and the Neumann boundary value problems of a class of Schr\\\"odinger equations, under the weak regularity assumption on the boundary of domains. As applications, gradient estimates of these solutions in Lebesgue spaces and Lorentz spaces are obtained.","authors_text":"Dachun Yang, Der-Chen Chang, Sibei Yang, Zunwei Fu","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-02T08:33:35Z","title":"Gradient Estimates via Rearrangements for Solutions of Some Schr\\\"odinger Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00612","kind":"arxiv","version":1},"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":"sha256:94f93fdb1c6ce8558b55cdb922b930782fe11b5e761b5de7ec758efe67319ba8","target":"record","created_at":"2026-05-18T01:19:43Z","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":"627b1ffdefe82b9b707a942737e8f02419fd1fa7557317d1382bea4b99804db6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-03-02T08:33:35Z","title_canon_sha256":"0eca1c9e5c1af13f841670381cb5907af1740ce4b133179b74d2384788f17cab"},"schema_version":"1.0","source":{"id":"1603.00612","kind":"arxiv","version":1}},"canonical_sha256":"7f129131441e6d86d3d85f522fdb71c915d0c65561c54e162d549c30e65c4955","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f129131441e6d86d3d85f522fdb71c915d0c65561c54e162d549c30e65c4955","first_computed_at":"2026-05-18T01:19:43.340989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:43.340989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q0lZbRv2vAIguI4cdqapqWsNuat5g0/08iQuFePU07qNa/QtxebK1pSw4Lo0Lf0U9NCA4yddTv5BHdgY+zzzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:43.341548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94f93fdb1c6ce8558b55cdb922b930782fe11b5e761b5de7ec758efe67319ba8","sha256:0f3b2e0a4ce81f46a317d11a8814613488199b027caaed8de3137077db88f70a"],"state_sha256":"d36ff8bd8537203b68ea060329698ce021ce1d238ba94c39df176027ac6f8170"}