{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2WLMBKJ5T4GXUXLCM4Z5CFKOCC","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":"b9c99fb27b4088cf36b2cd744238c6fbd182c039715d7cb9be7264a7d51fff15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-06T13:54:07Z","title_canon_sha256":"71d42a1c1c5676059d0a9ed200077ebf297f991f81e25e3fb414895cfa45fbe5"},"schema_version":"1.0","source":{"id":"1107.1132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1132","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1132v1","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1132","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"2WLMBKJ5T4GX","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2WLMBKJ5T4GXUXLC","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2WLMBKJ5","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:127fcbd4de0827a17f173e11f8a9de276fefa37b3218edec4cae3c1a486862cf","target":"graph","created_at":"2026-05-18T04:18:45Z","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":"We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W^{1,1}_0 distributional solution under suitable summability assumptions on the source in Lebesgue spaces. Moreover, we prove that our problem has no solution if the source is a Radon measure concentrated on a set of zero harmonic capacity.","authors_text":"Gisella Croce (LMAH), Lucio Boccardo, Luigi Orsina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-06T13:54:07Z","title":"A nonlinear degenerate elliptic problem with W^{1,1}_0 solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1132","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:a267c4e7d1bafad8cc24465f82e42d0a69a9d4f3a611b6d50a571fe55ef5796b","target":"record","created_at":"2026-05-18T04:18:45Z","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":"b9c99fb27b4088cf36b2cd744238c6fbd182c039715d7cb9be7264a7d51fff15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-06T13:54:07Z","title_canon_sha256":"71d42a1c1c5676059d0a9ed200077ebf297f991f81e25e3fb414895cfa45fbe5"},"schema_version":"1.0","source":{"id":"1107.1132","kind":"arxiv","version":1}},"canonical_sha256":"d596c0a93d9f0d7a5d626733d1154e10bc8670e67aa3f11054b22d9fc44d4bea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d596c0a93d9f0d7a5d626733d1154e10bc8670e67aa3f11054b22d9fc44d4bea","first_computed_at":"2026-05-18T04:18:45.521121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:45.521121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7e4wb+5t/9tvbVYxe9FEcJ8OrhSN5fCM9pSxf4jt4RqXst4scrtQSYi0NrmNGZGTJOR0l0YFnDEWy/OSKu8nDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:45.521633Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a267c4e7d1bafad8cc24465f82e42d0a69a9d4f3a611b6d50a571fe55ef5796b","sha256:127fcbd4de0827a17f173e11f8a9de276fefa37b3218edec4cae3c1a486862cf"],"state_sha256":"8ac312d529d838c33964fd2c048c12ed13c14f4ca21f94d3919018824e2f8ed9"}