{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PF2J76NZKU3VPPQYVWT3W7WMHS","short_pith_number":"pith:PF2J76NZ","schema_version":"1.0","canonical_sha256":"79749ff9b9553757be18ada7bb7ecc3cade5b679638b27c749427ae7c4f508f0","source":{"kind":"arxiv","id":"1206.3426","version":1},"attestation_state":"computed","paper":{"title":"A viscosity equation for minimizers of a class of very degenerate elliptic functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giulio Ciraolo","submitted_at":"2012-06-15T11:16:05Z","abstract_excerpt":"We consider the functional $$J(v) = \\int_\\Omega [f(|\\nabla v|) - v] dx,$$ where $\\Omega$ is a bounded domain and $f:[0,+\\infty)\\to \\mathbb{R}$ is a convex function vanishing for $s\\in [0,\\sigma]$, with $\\sigma>0$. We prove that a minimizer $u$ of $J$ satisfies an equation of the form $$\\min(F(\\nabla u, D^2 u), |\\nabla u|-\\sigma)=0$$ in the viscosity sense."},"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":"1206.3426","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-15T11:16:05Z","cross_cats_sorted":[],"title_canon_sha256":"477468f242a4858f6dac0de691a507a91711bcda91a7a17f9ffc579f10a532ef","abstract_canon_sha256":"9ea7f4be278f56863ce335e9a8a66a00003fb96ee9ab17cf23125c3714134564"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:30.320106Z","signature_b64":"vDmvqoab2vZi/7j8kBx2LDOh362z7keYBt3xsKSVbWzJCy7VdaPDWsGt35+jRp9YQiTnacgJSsAw8GMuZLh8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79749ff9b9553757be18ada7bb7ecc3cade5b679638b27c749427ae7c4f508f0","last_reissued_at":"2026-05-18T03:53:30.319461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:30.319461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A viscosity equation for minimizers of a class of very degenerate elliptic functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giulio Ciraolo","submitted_at":"2012-06-15T11:16:05Z","abstract_excerpt":"We consider the functional $$J(v) = \\int_\\Omega [f(|\\nabla v|) - v] dx,$$ where $\\Omega$ is a bounded domain and $f:[0,+\\infty)\\to \\mathbb{R}$ is a convex function vanishing for $s\\in [0,\\sigma]$, with $\\sigma>0$. We prove that a minimizer $u$ of $J$ satisfies an equation of the form $$\\min(F(\\nabla u, D^2 u), |\\nabla u|-\\sigma)=0$$ in the viscosity sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3426","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":"1206.3426","created_at":"2026-05-18T03:53:30.319551+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.3426v1","created_at":"2026-05-18T03:53:30.319551+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3426","created_at":"2026-05-18T03:53:30.319551+00:00"},{"alias_kind":"pith_short_12","alias_value":"PF2J76NZKU3V","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PF2J76NZKU3VPPQY","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PF2J76NZ","created_at":"2026-05-18T12:27:18.751474+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/PF2J76NZKU3VPPQYVWT3W7WMHS","json":"https://pith.science/pith/PF2J76NZKU3VPPQYVWT3W7WMHS.json","graph_json":"https://pith.science/api/pith-number/PF2J76NZKU3VPPQYVWT3W7WMHS/graph.json","events_json":"https://pith.science/api/pith-number/PF2J76NZKU3VPPQYVWT3W7WMHS/events.json","paper":"https://pith.science/paper/PF2J76NZ"},"agent_actions":{"view_html":"https://pith.science/pith/PF2J76NZKU3VPPQYVWT3W7WMHS","download_json":"https://pith.science/pith/PF2J76NZKU3VPPQYVWT3W7WMHS.json","view_paper":"https://pith.science/paper/PF2J76NZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.3426&json=true","fetch_graph":"https://pith.science/api/pith-number/PF2J76NZKU3VPPQYVWT3W7WMHS/graph.json","fetch_events":"https://pith.science/api/pith-number/PF2J76NZKU3VPPQYVWT3W7WMHS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PF2J76NZKU3VPPQYVWT3W7WMHS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PF2J76NZKU3VPPQYVWT3W7WMHS/action/storage_attestation","attest_author":"https://pith.science/pith/PF2J76NZKU3VPPQYVWT3W7WMHS/action/author_attestation","sign_citation":"https://pith.science/pith/PF2J76NZKU3VPPQYVWT3W7WMHS/action/citation_signature","submit_replication":"https://pith.science/pith/PF2J76NZKU3VPPQYVWT3W7WMHS/action/replication_record"}},"created_at":"2026-05-18T03:53:30.319551+00:00","updated_at":"2026-05-18T03:53:30.319551+00:00"}