{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4AJS2FAWQPF22K7WOZOA7BIB4G","short_pith_number":"pith:4AJS2FAW","schema_version":"1.0","canonical_sha256":"e0132d141683cbad2bf6765c0f8501e194958d4d115b2327417664a5000944bf","source":{"kind":"arxiv","id":"1902.05314","version":1},"attestation_state":"computed","paper":{"title":"Regularizing effect of the lower-order terms in elliptic problems with Orlicz growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Iwona Chlebicka","submitted_at":"2019-02-14T11:45:58Z","abstract_excerpt":"Under various conditions on the data we analyse how appearence of lower order terms affects the gradient estimates on solutions to a general nonlinear elliptic equation of the form \\[-{\\rm div}\\, a(x,Du)+b(x,u)=\\mu\\] with data $\\mu$ not belonging to the dual of the natural energy space but to Lorentz/Morrey-type spaces. The growth of the leading part of the operator is governed by a function of Orlicz-type, whereas the lower-order term satisfies the sign condition and is minorized with some convex function, whose speed of growth modulates the regularization of the solutions."},"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":"1902.05314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-14T11:45:58Z","cross_cats_sorted":[],"title_canon_sha256":"b2346ac268431a78649508212c26e6e2df281faeffdb1c85b7c4ece3907253fb","abstract_canon_sha256":"fe7788c44a000d0dff624b7e1d1ae0528bc477d72f12799045647fe72997d4ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:01.259045Z","signature_b64":"iDLGkm/tZglEYYVevKhbbrBGt3mkfxiVv6IlyTzBe5PbE1UBOxBPcJ1uFpUfj+Ft6MUaH5sAa1CW1sJ7UbBrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0132d141683cbad2bf6765c0f8501e194958d4d115b2327417664a5000944bf","last_reissued_at":"2026-05-17T23:54:01.258367Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:01.258367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularizing effect of the lower-order terms in elliptic problems with Orlicz growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Iwona Chlebicka","submitted_at":"2019-02-14T11:45:58Z","abstract_excerpt":"Under various conditions on the data we analyse how appearence of lower order terms affects the gradient estimates on solutions to a general nonlinear elliptic equation of the form \\[-{\\rm div}\\, a(x,Du)+b(x,u)=\\mu\\] with data $\\mu$ not belonging to the dual of the natural energy space but to Lorentz/Morrey-type spaces. The growth of the leading part of the operator is governed by a function of Orlicz-type, whereas the lower-order term satisfies the sign condition and is minorized with some convex function, whose speed of growth modulates the regularization of the solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05314","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":"1902.05314","created_at":"2026-05-17T23:54:01.258487+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.05314v1","created_at":"2026-05-17T23:54:01.258487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05314","created_at":"2026-05-17T23:54:01.258487+00:00"},{"alias_kind":"pith_short_12","alias_value":"4AJS2FAWQPF2","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"4AJS2FAWQPF22K7W","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"4AJS2FAW","created_at":"2026-05-18T12:33:10.108867+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/4AJS2FAWQPF22K7WOZOA7BIB4G","json":"https://pith.science/pith/4AJS2FAWQPF22K7WOZOA7BIB4G.json","graph_json":"https://pith.science/api/pith-number/4AJS2FAWQPF22K7WOZOA7BIB4G/graph.json","events_json":"https://pith.science/api/pith-number/4AJS2FAWQPF22K7WOZOA7BIB4G/events.json","paper":"https://pith.science/paper/4AJS2FAW"},"agent_actions":{"view_html":"https://pith.science/pith/4AJS2FAWQPF22K7WOZOA7BIB4G","download_json":"https://pith.science/pith/4AJS2FAWQPF22K7WOZOA7BIB4G.json","view_paper":"https://pith.science/paper/4AJS2FAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.05314&json=true","fetch_graph":"https://pith.science/api/pith-number/4AJS2FAWQPF22K7WOZOA7BIB4G/graph.json","fetch_events":"https://pith.science/api/pith-number/4AJS2FAWQPF22K7WOZOA7BIB4G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4AJS2FAWQPF22K7WOZOA7BIB4G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4AJS2FAWQPF22K7WOZOA7BIB4G/action/storage_attestation","attest_author":"https://pith.science/pith/4AJS2FAWQPF22K7WOZOA7BIB4G/action/author_attestation","sign_citation":"https://pith.science/pith/4AJS2FAWQPF22K7WOZOA7BIB4G/action/citation_signature","submit_replication":"https://pith.science/pith/4AJS2FAWQPF22K7WOZOA7BIB4G/action/replication_record"}},"created_at":"2026-05-17T23:54:01.258487+00:00","updated_at":"2026-05-17T23:54:01.258487+00:00"}