{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VIN3YF2GMAGPF47C6HO76CWI77","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":"bc0ea48c79ebfe1436a2fa6626f8613bac688b864e2bd88e1d1dca4ad4f25472","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-28T08:31:24Z","title_canon_sha256":"597c807b942b2d8ab5b14a27234745766a12a64e44c2d45140c28a3cf497d4ca"},"schema_version":"1.0","source":{"id":"1211.6542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.6542","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1211.6542v2","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.6542","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"VIN3YF2GMAGP","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VIN3YF2GMAGPF47C","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VIN3YF2G","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:8b5396842c6483f6831af0a2e2c37d854b3b64b2f598c1d8378b1875a416d513","target":"graph","created_at":"2026-05-18T03:33:49Z","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":"Let $\\Omega \\subset \\mathbb{R}^{N}$ be a smooth bounded domain, $H$ a Caratheodory function defined in $\\Omega \\times \\mathbb{R\\times R}^{N},$ and $\\mu $ a bounded Radon measure in $\\Omega .$ We study the problem% \\begin{equation*} -\\Delta_{p}u+H(x,u,\\nabla u)=\\mu \\quad \\text{in}\\Omega,\\qquad u=0\\quad \\text{on}\\partial \\Omega, \\end{equation*} where $\\Delta_{p}$ is the $p$-Laplacian ($p>1$)$,$ and we emphasize the case $H(x,u,\\nabla u)=\\pm \\left\\| \\nabla u\\right\\| ^{q}$ ($q>0$). We obtain an existence result under subcritical growth assumptions on $H,$ we give necessary conditions of existence ","authors_text":"Laurent Veron (LMPT), Marie-Fran\\c{c}oise Bidaut-V\\'eron (LMPT), Marta Garcia-Huidobro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-28T08:31:24Z","title":"Remarks on some quasilinear equations with gradient terms and measure data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6542","kind":"arxiv","version":2},"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:d01ccbe052cf34d04120796bbe29c535d3bcf02f6c277495463dec0859c66a4e","target":"record","created_at":"2026-05-18T03:33:49Z","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":"bc0ea48c79ebfe1436a2fa6626f8613bac688b864e2bd88e1d1dca4ad4f25472","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-28T08:31:24Z","title_canon_sha256":"597c807b942b2d8ab5b14a27234745766a12a64e44c2d45140c28a3cf497d4ca"},"schema_version":"1.0","source":{"id":"1211.6542","kind":"arxiv","version":2}},"canonical_sha256":"aa1bbc1746600cf2f3e2f1ddff0ac8ffdf690994cca91fcd54308c81d539d3dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa1bbc1746600cf2f3e2f1ddff0ac8ffdf690994cca91fcd54308c81d539d3dd","first_computed_at":"2026-05-18T03:33:49.655114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:49.655114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tHzyEwQ9mvCXfMKxUZh7gypXJowblSVcRl5l1M7rPtmTzAnN/w4hOxwFLtR07Ozj40WdgYEMxUSw7ne09fXiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:49.656967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.6542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d01ccbe052cf34d04120796bbe29c535d3bcf02f6c277495463dec0859c66a4e","sha256:8b5396842c6483f6831af0a2e2c37d854b3b64b2f598c1d8378b1875a416d513"],"state_sha256":"79bde7d4a63706fc8329c2fb8c134a83f2b34c1bd29be0c90476fcedb3278197"}