{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LDXVY5A3LHH3P3CIAS3E4SX25R","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":"b209c9e94bc5f2168cf2be829a8a077801f1684a0b2c88f567652a5ac3e42187","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-13T18:03:55Z","title_canon_sha256":"7c2e73a16792ffbff0ea85964ec90c87cfc28d96c0d94c5cd4a1c4bb490759d4"},"schema_version":"1.0","source":{"id":"1204.3063","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3063","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3063v2","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3063","created_at":"2026-05-18T03:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"LDXVY5A3LHH3","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LDXVY5A3LHH3P3CI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LDXVY5A3","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:cfcaa2ca682277a290a3cbc382df443a7f3688015f983b1ae09daf2de1de801c","target":"graph","created_at":"2026-05-18T03:41:58Z","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 introduce a class of weak solutions to the quasilinear equation $-\\Delta_p u = \\sigma |u|^{p-2}u$ in an open set $\\Omega\\subset\\mathbf{R}^n$. Here $p>1$, and $\\Delta_p u$ is the $p$-Laplacian operator. Our notion of solution is tailored to general distributional coefficients $\\sigma$ satisfying a certain weighted Sobolev-Poincare inequality. We also study weak solutions of the closely related equation $-\\Delta_p v = (p-1)|\\nabla v|^p + \\sigma$, under the same conditions on $\\sigma$. Our results for this latter equation will allow us to characterize the class of distributions $\\sigma$ which ","authors_text":"Benjamin J. Jaye, Igor E. Verbitsky, Vladimir G. Maz'ya","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-13T18:03:55Z","title":"Quasilinear elliptic equations and weighted Sobolev-Poincar\\'{e} inequalities with distributional weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3063","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":"sha256:496aca65ee7f4ea74c42e4313e50a98d219d5eb83134ee129aac46e0b6bdac04","target":"record","created_at":"2026-05-18T03:41:58Z","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":"b209c9e94bc5f2168cf2be829a8a077801f1684a0b2c88f567652a5ac3e42187","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-13T18:03:55Z","title_canon_sha256":"7c2e73a16792ffbff0ea85964ec90c87cfc28d96c0d94c5cd4a1c4bb490759d4"},"schema_version":"1.0","source":{"id":"1204.3063","kind":"arxiv","version":2}},"canonical_sha256":"58ef5c741b59cfb7ec4804b64e4afaec73aa934f4066ed10b6b540faa34343b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58ef5c741b59cfb7ec4804b64e4afaec73aa934f4066ed10b6b540faa34343b2","first_computed_at":"2026-05-18T03:41:58.717838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:58.717838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UsMXTbMAppwpMijg6Z/cYplt+QDmCj99UQdvlxUMgjxOuUd5giYoSq8yb92Ef/2TiIIZqDmjrBBN/JZwyX9JCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:58.718713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3063","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:496aca65ee7f4ea74c42e4313e50a98d219d5eb83134ee129aac46e0b6bdac04","sha256:cfcaa2ca682277a290a3cbc382df443a7f3688015f983b1ae09daf2de1de801c"],"state_sha256":"8e77981c43606bbeca8c98fa41d70865d886e73584eeb92538ea456361425cb0"}