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The associated equation, coined the $\\infty$-Bilaplacian, is a \\emph{third order} fully nonlinear PDE given by $\\Delta^2_\\infty u\\, := (\\Delta u)^3 | D (\\Delta u) |^2 = 0.$ In this work we build a numerical method aimed at quantifying the nature of solutions to this problem which we call $\\infty$-Biharmonic functions. For fixed $p$ we design a mixed finite element scheme for the pre-limiting equation, the $p$-Bilaplacian $\\Delta^2_p u\\, := \\Delta(| \\Delta u |^{p-2} \\Delta u) = 0.$ We prove c"},"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":"1701.07415","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-25T18:20:29Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0c118c2bc1997de8dc5c6f8d21922ee7a78ae97d43c446d2e7251f2fe7f69538","abstract_canon_sha256":"62af716825e7012910b42b85af971dd92531c2ec999f59b9430b2233ff21a501"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:09.355351Z","signature_b64":"LWo2eCe7bjuIHMJSXrc+YWYXI+3gRUmHZs2mH+70dwSQ/PfhDQGh2EZW0O2I89d37wVFVfH/6bVsptaLjBkKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5fd0ac36611f25096e30472012fa12b5fb27bfdf85febaf66b4793e34a992c1","last_reissued_at":"2026-05-18T00:16:09.354623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:09.354623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the numerical approximation of $p$-Biharmonic and $\\infty$-Biharmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Nikos Katzourakis (Reading, Tristan Pryer (Reading, UK)","submitted_at":"2017-01-25T18:20:29Z","abstract_excerpt":"In [KP16] (arXiv:1605.07880) the authors introduced a second-order variational problem in $L^{\\infty}$. 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For fixed $p$ we design a mixed finite element scheme for the pre-limiting equation, the $p$-Bilaplacian $\\Delta^2_p u\\, := \\Delta(| \\Delta u |^{p-2} \\Delta u) = 0.$ We prove c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07415","kind":"arxiv","version":2},"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":"1701.07415","created_at":"2026-05-18T00:16:09.354730+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.07415v2","created_at":"2026-05-18T00:16:09.354730+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07415","created_at":"2026-05-18T00:16:09.354730+00:00"},{"alias_kind":"pith_short_12","alias_value":"4X6QVQ3GCHZF","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4X6QVQ3GCHZFBFXD","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4X6QVQ3G","created_at":"2026-05-18T12:31:00.734936+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/4X6QVQ3GCHZFBFXDARZACL5BFN","json":"https://pith.science/pith/4X6QVQ3GCHZFBFXDARZACL5BFN.json","graph_json":"https://pith.science/api/pith-number/4X6QVQ3GCHZFBFXDARZACL5BFN/graph.json","events_json":"https://pith.science/api/pith-number/4X6QVQ3GCHZFBFXDARZACL5BFN/events.json","paper":"https://pith.science/paper/4X6QVQ3G"},"agent_actions":{"view_html":"https://pith.science/pith/4X6QVQ3GCHZFBFXDARZACL5BFN","download_json":"https://pith.science/pith/4X6QVQ3GCHZFBFXDARZACL5BFN.json","view_paper":"https://pith.science/paper/4X6QVQ3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.07415&json=true","fetch_graph":"https://pith.science/api/pith-number/4X6QVQ3GCHZFBFXDARZACL5BFN/graph.json","fetch_events":"https://pith.science/api/pith-number/4X6QVQ3GCHZFBFXDARZACL5BFN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4X6QVQ3GCHZFBFXDARZACL5BFN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4X6QVQ3GCHZFBFXDARZACL5BFN/action/storage_attestation","attest_author":"https://pith.science/pith/4X6QVQ3GCHZFBFXDARZACL5BFN/action/author_attestation","sign_citation":"https://pith.science/pith/4X6QVQ3GCHZFBFXDARZACL5BFN/action/citation_signature","submit_replication":"https://pith.science/pith/4X6QVQ3GCHZFBFXDARZACL5BFN/action/replication_record"}},"created_at":"2026-05-18T00:16:09.354730+00:00","updated_at":"2026-05-18T00:16:09.354730+00:00"}