{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:I7C2DH2TY4SORV5PVNNY2M3CKY","short_pith_number":"pith:I7C2DH2T","schema_version":"1.0","canonical_sha256":"47c5a19f53c724e8d7afab5b8d3362560cc843c3c055a55d560659fe1b918f4d","source":{"kind":"arxiv","id":"1512.08160","version":2},"attestation_state":"computed","paper":{"title":"Regularity for a quasilinear continuous casting problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram Karakhanyan","submitted_at":"2015-12-27T01:19:03Z","abstract_excerpt":"In this paper study the regularity of continuous casting problem \\begin{equation} \\hbox{div}(|\\nabla u|^{p-2}\\nabla u-{\\bf v} \\beta(u))=0\\tag{$\\sharp$} \\end{equation} for prescribed constant velocity $\\bf v$ and enthalpy $\\beta(u)$ with jump discontinuity at $u=0$. We establish the following estimates: local log-Lipschitz $p>2$ for $u$ (and BMO for $\\nabla u$) for two phase, Lipschitz $p>1$ for one phase and linear growth up-to boundary near the contact points. We also prove that the free boundary is continuous curve in the direction of $\\bf v$ in two spatial dimensions. The proof is based on "},"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":"1512.08160","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-27T01:19:03Z","cross_cats_sorted":[],"title_canon_sha256":"3fe6579d6680ba0da3729229d82466056baf67c4825635b3ae1d34e25eb17686","abstract_canon_sha256":"e8f11d557a620674d4c97f505defa36dc112a2b5a46aad8e0762d3c9af704122"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:35.069598Z","signature_b64":"6sE4sYzG1031dWvyrKL9ZNMCxJwdIu/c2pYyEQDqptmNCyaOucKPPa2w+EewVaWTArhuAM4xQPafQCxw+P+SCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47c5a19f53c724e8d7afab5b8d3362560cc843c3c055a55d560659fe1b918f4d","last_reissued_at":"2026-05-18T00:45:35.069094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:35.069094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity for a quasilinear continuous casting problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aram Karakhanyan","submitted_at":"2015-12-27T01:19:03Z","abstract_excerpt":"In this paper study the regularity of continuous casting problem \\begin{equation} \\hbox{div}(|\\nabla u|^{p-2}\\nabla u-{\\bf v} \\beta(u))=0\\tag{$\\sharp$} \\end{equation} for prescribed constant velocity $\\bf v$ and enthalpy $\\beta(u)$ with jump discontinuity at $u=0$. We establish the following estimates: local log-Lipschitz $p>2$ for $u$ (and BMO for $\\nabla u$) for two phase, Lipschitz $p>1$ for one phase and linear growth up-to boundary near the contact points. We also prove that the free boundary is continuous curve in the direction of $\\bf v$ in two spatial dimensions. The proof is based on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08160","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":"1512.08160","created_at":"2026-05-18T00:45:35.069168+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.08160v2","created_at":"2026-05-18T00:45:35.069168+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08160","created_at":"2026-05-18T00:45:35.069168+00:00"},{"alias_kind":"pith_short_12","alias_value":"I7C2DH2TY4SO","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"I7C2DH2TY4SORV5P","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"I7C2DH2T","created_at":"2026-05-18T12:29:25.134429+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/I7C2DH2TY4SORV5PVNNY2M3CKY","json":"https://pith.science/pith/I7C2DH2TY4SORV5PVNNY2M3CKY.json","graph_json":"https://pith.science/api/pith-number/I7C2DH2TY4SORV5PVNNY2M3CKY/graph.json","events_json":"https://pith.science/api/pith-number/I7C2DH2TY4SORV5PVNNY2M3CKY/events.json","paper":"https://pith.science/paper/I7C2DH2T"},"agent_actions":{"view_html":"https://pith.science/pith/I7C2DH2TY4SORV5PVNNY2M3CKY","download_json":"https://pith.science/pith/I7C2DH2TY4SORV5PVNNY2M3CKY.json","view_paper":"https://pith.science/paper/I7C2DH2T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.08160&json=true","fetch_graph":"https://pith.science/api/pith-number/I7C2DH2TY4SORV5PVNNY2M3CKY/graph.json","fetch_events":"https://pith.science/api/pith-number/I7C2DH2TY4SORV5PVNNY2M3CKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I7C2DH2TY4SORV5PVNNY2M3CKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I7C2DH2TY4SORV5PVNNY2M3CKY/action/storage_attestation","attest_author":"https://pith.science/pith/I7C2DH2TY4SORV5PVNNY2M3CKY/action/author_attestation","sign_citation":"https://pith.science/pith/I7C2DH2TY4SORV5PVNNY2M3CKY/action/citation_signature","submit_replication":"https://pith.science/pith/I7C2DH2TY4SORV5PVNNY2M3CKY/action/replication_record"}},"created_at":"2026-05-18T00:45:35.069168+00:00","updated_at":"2026-05-18T00:45:35.069168+00:00"}